{"id":8939,"date":"2017-04-27T21:25:21","date_gmt":"2017-04-27T21:25:21","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=8939"},"modified":"2020-07-02T05:42:54","modified_gmt":"2020-07-02T05:42:54","slug":"problem-set-geometry","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/problem-set-geometry\/","title":{"raw":"Problem Set: Geometry","rendered":"Problem Set: Geometry"},"content":{"raw":"

Practice Makes Perfect<\/h2>\r\nUse the Properties of Angles<\/strong>\r\nIn the following exercises, find \u24d0 the supplement and \u24d1 the complement of the given angle.<\/strong>\r\n\r\n[latex]{53^\\circ }[\/latex]\r\n\r\n[reveal-answer q=\"229213\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229213\"]\r\n\r\n\u24d0 127\u00b0\r\n\u24d1 37\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\n[latex]{16^\\circ }[\/latex]\r\n\r\n[latex]{29^\\circ }[\/latex]\r\n\r\n[reveal-answer q=\"229215\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229215\"]\r\n\r\n\u24d0 151\u00b0\r\n\u24d1 61\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\n[latex]{72^\\circ }[\/latex]\r\n\r\nIn the following exercises, use the properties of angles to solve.<\/strong>\r\n\r\nFind the supplement of a [latex]{135^\\circ }[\/latex] angle.\r\n\r\n[reveal-answer q=\"239212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"239212\"]\r\n\r\n45\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nFind the complement of a [latex]{38^\\circ }[\/latex] angle.\r\n\r\nFind the complement of a [latex]27.5^\\circ [\/latex] angle.\r\n\r\n[reveal-answer q=\"329212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"329212\"]\r\n\r\n62.5\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nFind the supplement of a [latex]109.5^\\circ [\/latex] angle.\r\n\r\nTwo angles are supplementary. The larger angle is [latex]{56^\\circ }[\/latex] more than the smaller angle. Find the measures of both angles.\r\n\r\n[reveal-answer q=\"249212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"249212\"]\r\n\r\n62\u00b0, 118\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nTwo angles are supplementary. The smaller angle is [latex]{36^\\circ }[\/latex] less than the larger angle. Find the measures of both angles.\r\n\r\nTwo angles are complementary. The smaller angle is [latex]{34^\\circ }[\/latex] less than the larger angle. Find the measures of both angles.\r\n\r\n[reveal-answer q=\"269212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"269212\"]\r\n\r\n62\u00b0, 28\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nTwo angles are complementary. The larger angle is [latex]{52^\\circ }[\/latex] more than the smaller angle. Find the measures of both angles.\r\n\r\nUse the Properties of Triangles<\/strong>\r\n\r\nIn the following exercises, solve using properties of triangles<\/strong>.\r\n\r\nThe measures of two angles of a triangle are [latex]{26^\\circ }[\/latex] and [latex]{98^\\circ }[\/latex]. Find the measure of the third angle.\r\n\r\n[reveal-answer q=\"279212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"279212\"]\r\n\r\n56\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nThe measures of two angles of a triangle are [latex]{61^\\circ }[\/latex] and [latex]{84^\\circ }[\/latex]. Find the measure of the third angle.\r\n\r\nThe measures of two angles of a triangle are [latex]{105^\\circ }[\/latex] and [latex]{31^\\circ }[\/latex]. Find the measure of the third angle.\r\n\r\n[reveal-answer q=\"289212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"289212\"]\r\n\r\n44\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nThe measures of two angles of a triangle are [latex]{47^\\circ }[\/latex] and [latex]{72^\\circ }[\/latex]. Find the measure of the third angle.\r\n\r\nOne angle of a right triangle measures [latex]{33^\\circ }[\/latex]. What is the measure of the other angle?\r\n\r\n[reveal-answer q=\"228212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"228212\"]\r\n\r\n57\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nOne angle of a right triangle measures [latex]{51^\\circ }[\/latex]. What is the measure of the other angle?\r\n\r\nOne angle of a right triangle measures [latex]22.5^\\circ [\/latex]. What is the measure of the other angle?\r\n\r\n[reveal-answer q=\"227212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"227212\"]\r\n\r\n67.5\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nOne angle of a right triangle measures [latex]36.5^\\circ [\/latex]. What is the measure of the other angle?\r\n\r\nThe two smaller angles of a right triangle have equal measures. Find the measures of all three angles.\r\n\r\n[reveal-answer q=\"226212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"226212\"]\r\n\r\n45\u00b0, 45\u00b0, 90\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nThe measure of the smallest angle of a right triangle is [latex]{20^\\circ }[\/latex] less than the measure of the other small angle. Find the measures of all three angles.\r\n\r\nThe angles in a triangle are such that the measure of one angle is twice the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.\r\n\r\n[reveal-answer q=\"225212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225212\"]\r\n\r\n30\u00b0, 60\u00b0, 90\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nThe angles in a triangle are such that the measure of one angle is [latex]{20^\\circ }[\/latex] more than the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.\r\n\r\nFind the Length of the Missing Side<\/strong>\r\n\r\nIn the following exercises, [latex]\\Delta ABC[\/latex] is similar to [latex]\\Delta XYZ[\/latex]. Find the length of the indicated side.<\/strong>\r\n\r\n\"Two\r\n\r\nside [latex]b[\/latex]\r\n\r\n[reveal-answer q=\"225312\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225312\"]\r\n\r\n12\r\n\r\n[\/hidden-answer]\r\n\r\nside [latex]x[\/latex]\r\n\r\nOn a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides are shown in the figure below. The actual distance from Los Angeles to Las Vegas is [latex]270[\/latex] miles.\r\n\r\n\"A\r\n\r\nFind the distance from Los Angeles to San Francisco.\r\n\r\n[reveal-answer q=\"339212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"339212\"]\r\n\r\n351 miles\r\n\r\n[\/hidden-answer]\r\n\r\nFind the distance from San Francisco to Las Vegas.\r\n\r\nUse the Pythagorean Theorem<\/strong>\r\n\r\nIn the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse<\/strong>.\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"449212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"449212\"]\r\n\r\n15\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"5529212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=5529212\"]\r\n\r\n25\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\nFind the Length of the Missing Side<\/strong>\r\n\r\nIn the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.<\/strong>\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"669212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"669212\"]\r\n\r\n8\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"225512\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225512\"]\r\n\r\n12\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"229332\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229332\"]\r\n\r\n10.2\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"288212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"288212\"]\r\n\r\n8\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\nIn the following exercises, solve. Approximate to the nearest tenth, if necessary.<\/strong>\r\n\r\nA [latex]\\text{13-foot}[\/latex] string of lights will be attached to the top of a [latex]\\text{12-foot}[\/latex] pole for a holiday display. How far from the base of the pole should the end of the string of lights be anchored?\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"229452\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229452\"]\r\n\r\n5 feet\r\n\r\n[\/hidden-answer]\r\n\r\nPam wants to put a banner across her garage door to congratulate her son on his college graduation. The garage door is [latex]12[\/latex] feet high and [latex]16[\/latex] feet wide. How long should the banner be to fit the garage door?\r\n\r\n\"A\r\n\r\nChi is planning to put a path of paving stones through her flower garden. The flower garden is a square with sides of [latex]10[\/latex] feet. What will the length of the path be?\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"234212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"234212\"]\r\n\r\n14.1 feet\r\n\r\n[\/hidden-answer]\r\n\r\nBrian borrowed a [latex]\\text{20-foot}[\/latex] extension ladder to paint his house. If he sets the base of the ladder [latex]6[\/latex] feet from the house, how far up will the top of the ladder reach?\r\n\r\n\"A\r\n

Everyday Math<\/h2>\r\nBuilding a scale model<\/strong> Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is [latex]30[\/latex] feet wide and [latex]35[\/latex] feet tall at the highest point of the roof. If the dollhouse will be [latex]2.5[\/latex] feet wide, how tall will its highest point be?\r\n\r\n[reveal-answer q=\"222112\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"222112\"]\r\n\r\n2.9 feet\r\n\r\n[\/hidden-answer]\r\n\r\nMeasurement<\/strong> A city engineer plans to build a footbridge across a lake from point [latex]\\text{X}[\/latex] to point [latex]\\text{Y}[\/latex], as shown in the picture below. To find the length of the footbridge, she draws a right triangle [latex]\\text{XYZ}[\/latex], with right angle at [latex]\\text{X}[\/latex]. She measures the distance from [latex]\\text{X}[\/latex] to [latex]\\text{Z},800[\/latex] feet, and from [latex]\\text{Y}[\/latex] to [latex]\\text{Z},1,000[\/latex] feet. How long will the bridge be?\r\n\r\n\"A\r\n

Writing Exercises<\/h2>\r\nWrite three of the properties of triangles from this section and then explain each in your own words.\r\n\r\nAnswers will vary.\r\n\r\nExplain how the figure below illustrates the Pythagorean Theorem for a triangle with legs of length [latex]3[\/latex] and [latex]4[\/latex].\r\n\r\n\"Three\r\n

Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\".\"\r\n\u24d1 What does this checklist tell you about your mastery of this section? What steps will you take to improve?\r\n

<\/h2>\r\n

Use Properties of Angles, Triangles, and the Pythagorean Theorem<\/h2>\r\nUse Properties of Angles<\/strong>\r\nIn the following exercises, solve using properties of angles.\r\n\r\nWhat is the supplement of a [latex]{48^\\circ }[\/latex] angle?\r\n\r\n[reveal-answer q=\"133456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"133456\"]\r\n\r\n132\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nWhat is the complement of a [latex]{61^\\circ }[\/latex] angle?\r\n\r\nTwo angles are complementary. The smaller angle is [latex]{24^\\circ }[\/latex] less than the larger angle. Find the measures of both angles.\r\n\r\n[reveal-answer q=\"879212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"879212\"]\r\n\r\n33\u00b0, 57\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nTwo angles are supplementary. The larger angle is [latex]{45^\\circ }[\/latex] more than the smaller angle. Find the measures of both angles.\r\n\r\nUse Properties of Triangles<\/strong>\r\nIn the following exercises, solve using properties of triangles.<\/strong>\r\n\r\nThe measures of two angles of a triangle are [latex]22[\/latex] and [latex]85[\/latex] degrees. Find the measure of the third angle.\r\n\r\n[reveal-answer q=\"229333\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229333\"]\r\n\r\n73\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nOne angle of a right triangle measures [latex]41.5[\/latex] degrees. What is the measure of the other small angle?\r\n\r\nOne angle of a triangle is [latex]{30^\\circ }[\/latex] more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.\r\n\r\n[reveal-answer q=\"277712\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"277712\"]\r\n\r\n30\u00b0, 60\u00b0, 90\u00b0\r\n\r\n[\/hidden-answer]\r\n\r\nOne angle of a triangle is twice the measure of the smallest angle. The third angle is [latex]{60^\\circ }[\/latex] more than the measure of the smallest angle. Find the measures of all three angles.\r\n\r\nIn the following exercises, [latex]\\Delta ABC[\/latex] is similar to [latex]\\Delta XYZ[\/latex]. Find the length of the indicated side.<\/strong>\r\n\r\n\"Two\r\n\r\nside [latex]x[\/latex]\r\n\r\n[reveal-answer q=\"238212\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"238212\"]\r\n\r\n15\r\n\r\n[\/hidden-answer]\r\n\r\nside [latex]b[\/latex]\r\n\r\nUse the Pythagorean Theorem<\/strong>\r\nIn the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.<\/strong>\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"212312\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"212312\"]\r\n\r\n26\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"265412\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"265412\"]\r\n\r\n8\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"229882\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229882\"]\r\n\r\n8.1\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\nIn the following exercises, solve. Approximate to the nearest tenth, if necessary.<\/strong>\r\n\r\nSergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is [latex]8[\/latex] feet tall and Sergio has [latex]10[\/latex] feet of wire. How far from the base of the antenna can he attach the wire?\r\n\r\n\"An\r\n\r\n[reveal-answer q=\"255512\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"255512\"]\r\n\r\n6 feet\r\n\r\n[\/hidden-answer]\r\n\r\nSeong is building shelving in his garage. The shelves are [latex]36[\/latex] inches wide and [latex]15[\/latex] inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?\r\n\r\n\"A\r\n

Use Properties of Rectangles, Triangles, and Trapezoids<\/h2>\r\nUnderstand Linear, Square, Cubic Measure<\/strong>\r\nIn the following exercises, would you measure each item using linear, square, or cubic measure?<\/strong>\r\n\r\namount of sand in a sandbag\r\n\r\n[reveal-answer q=\"225612\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225612\"]\r\n\r\ncubic\r\n\r\n[\/hidden-answer]\r\n\r\nheight of a tree\r\n\r\nsize of a patio\r\n\r\n[reveal-answer q=\"228112\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"228112\"]\r\n\r\nsquare\r\n\r\n[\/hidden-answer]\r\n\r\nlength of a highway\r\n\r\nIn the following exercises, find<\/strong>\r\n\r\n\u24d0 the perimeter<\/strong>\r\n\u24d1 the area of each figure<\/strong>\r\n\r\n\"Three\r\n\r\n\u24d0 8 units\r\n\u24d1 3 sq. units\r\n\r\n\"Five\r\n\r\nUse Properties of Rectangles<\/strong>\r\n\r\nIn the following exercises, find the<\/strong>\r\n\r\n\u24d0 perimeter<\/strong>\r\n\u24d1 area of each rectangle<\/strong>\r\n\r\nThe length of a rectangle is [latex]42[\/latex] meters and the width is [latex]28[\/latex] meters.\r\n\r\n[reveal-answer q=\"228312\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"228312\"]\r\n\r\n\u24d0 140 m\r\n\u24d1 1176 sq. m\r\n\r\n[\/hidden-answer]\r\n\r\nThe length of a rectangle is [latex]36[\/latex] feet and the width is [latex]19[\/latex] feet.\r\n\r\nA sidewalk in front of Kathy\u2019s house is in the shape of a rectangle [latex]4[\/latex] feet wide by [latex]45[\/latex] feet long.\r\n\r\n[reveal-answer q=\"223412\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"223412\"]\r\n\r\n\u24d0 98 ft.\r\n\u24d1 180 sq. ft.\r\n\r\n[\/hidden-answer]\r\n\r\nA rectangular room is [latex]16[\/latex] feet wide by [latex]12[\/latex] feet long.\r\n\r\nIn the following exercises, solve.<\/strong>\r\n\r\nFind the length of a rectangle with perimeter of [latex]220[\/latex] centimeters and width of [latex]85[\/latex] centimeters.\r\n\r\n[reveal-answer q=\"223332\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"223332\"]\r\n\r\n25 cm\r\n\r\n[\/hidden-answer]\r\n\r\nFind the width of a rectangle with perimeter [latex]39[\/latex] and length [latex]11[\/latex].\r\n\r\nThe area of a rectangle is [latex]2356[\/latex] square meters. The length is [latex]38[\/latex] meters. What is the width?\r\n\r\n[reveal-answer q=\"220012\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"220012\"]\r\n\r\n62 m\r\n\r\n[\/hidden-answer]\r\n\r\nThe width of a rectangle is [latex]45[\/latex] centimeters. The area is [latex]2700[\/latex] square centimeters. What is the length?\r\n\r\nThe length of a rectangle is [latex]12[\/latex] centimeters more than the width. The perimeter is [latex]74[\/latex] centimeters. Find the length and the width.\r\n\r\n[reveal-answer q=\"123456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123456\"]\r\n\r\n24.5 in., 12.5 in.\r\n\r\n[\/hidden-answer]\r\n\r\nThe width of a rectangle is [latex]3[\/latex] more than twice the length. The perimeter is [latex]96[\/latex] inches. Find the length and the width.\r\n\r\nUse Properties of Triangles<\/strong>\r\nIn the following exercises, solve using the properties of triangles.\r\n\r\nFind the area of a triangle with base [latex]18[\/latex] inches and height [latex]15[\/latex] inches.\r\n\r\n[reveal-answer q=\"223456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"223456\"]\r\n\r\n135 sq. in.\r\n\r\n[\/hidden-answer]\r\n\r\nFind the area of a triangle with base [latex]33[\/latex] centimeters and height [latex]21[\/latex] centimeters.\r\n\r\nA triangular road sign has base [latex]30[\/latex] inches and height [latex]40[\/latex] inches. What is its area?\r\n\r\n[reveal-answer q=\"323456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"323456\"]\r\n\r\n600 sq. in.\r\n\r\n[\/hidden-answer]\r\n\r\nIf a triangular courtyard has sides [latex]9[\/latex] feet and [latex]12[\/latex] feet and the perimeter is [latex]32[\/latex] feet, how long is the third side?\r\n\r\nA tile in the shape of an isosceles triangle has a base of [latex]6[\/latex] inches. If the perimeter is [latex]20[\/latex] inches, find the length of each of the other sides.\r\n\r\n[reveal-answer q=\"423456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"423456\"]\r\n\r\n7 in., 7 in.\r\n\r\n[\/hidden-answer]\r\n\r\nFind the length of each side of an equilateral triangle with perimeter of [latex]81[\/latex] yards.\r\n\r\nThe perimeter of a triangle is [latex]59[\/latex] feet. One side of the triangle is [latex]3[\/latex] feet longer than the shortest side. The third side is [latex]5[\/latex] feet longer than the shortest side. Find the length of each side.\r\n\r\n[reveal-answer q=\"523456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"523456\"]\r\n\r\n17 ft., 20 ft., 22 ft.\r\n\r\n[\/hidden-answer]\r\n\r\nOne side of a triangle is three times the smallest side. The third side is [latex]9[\/latex] feet more than the shortest side. The perimeter is [latex]39[\/latex] feet. Find the lengths of all three sides.\r\n\r\nUse Properties of Trapezoids<\/strong>\r\nIn the following exercises, solve using the properties of trapezoids.<\/strong>\r\n\r\nThe height of a trapezoid is [latex]8[\/latex] feet and the bases are [latex]11[\/latex] and [latex]14[\/latex] feet. What is the area?\r\n\r\n[reveal-answer q=\"623456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"623456\"]\r\n\r\n100 sq. ft.\r\n\r\n[\/hidden-answer]\r\n\r\nThe height of a trapezoid is [latex]5[\/latex] yards and the bases are [latex]7[\/latex] and [latex]10[\/latex] yards. What is the area?\r\n\r\nFind the area of the trapezoid with height [latex]25[\/latex] meters and bases [latex]32.5[\/latex] and [latex]21.5[\/latex] meters.\r\n\r\n[reveal-answer q=\"723456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"723456\"]\r\n\r\n675 sq. m\r\n\r\n[\/hidden-answer]\r\n\r\nA flag is shaped like a trapezoid with height [latex]62[\/latex] centimeters and the bases are [latex]91.5[\/latex] and [latex]78.1[\/latex] centimeters. What is the area of the flag?\r\n

Practice Makes Perfect<\/h2>\r\nUnderstand Linear, Square, and Cubic Measure<\/strong>\r\nIn the following exercises, determine whether you would measure each item using linear, square, or cubic units.<\/strong>\r\n\r\namount of water in a fish tank\r\n\r\n[reveal-answer q=\"124456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"124456\"]\r\n\r\ncubic\r\n\r\n[\/hidden-answer]\r\n\r\nlength of dental floss\r\n\r\nliving area of an apartment\r\n\r\n[reveal-answer q=\"125456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"125456\"]\r\n\r\nsquare\r\n\r\n[\/hidden-answer]\r\n\r\nfloor space of a bathroom tile\r\n\r\nheight of a doorway\r\n\r\n[reveal-answer q=\"126456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"126456\"]\r\n\r\nlinear\r\n\r\n[\/hidden-answer]\r\n\r\ncapacity of a truck trailer\r\n\r\nIn the following exercises, find the \u24d0 perimeter and \u24d1 area of each figure. Assume each side of the square is [latex]1[\/latex] cm.<\/strong>\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"127456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"127456\"]\r\n\r\n\u24d0 10 cm\r\n\u24d1 4 sq. cm\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"Three\r\n\r\n[reveal-answer q=\"128456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"128456\"]\r\n\r\n\u24d0 8 cm\r\n\u24d1 3 sq. cm\r\n\r\n[\/hidden-answer]\r\n\r\n\"Four\r\n\r\n\"Five\r\n\r\n[reveal-answer q=\"129456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"129456\"]\r\n\r\n\u24d0 10 cm\r\n\u24d1 5 sq. cm\r\n\r\n[\/hidden-answer]\r\n\r\n\"A\r\n\r\nUse the Properties of Rectangles<\/strong>\r\nIn the following exercises, find the \u24d0 perimeter and \u24d1 area of each rectangle.<\/strong>\r\n\r\nThe length of a rectangle is [latex]85[\/latex] feet and the width is [latex]45[\/latex] feet.\r\n\r\n[reveal-answer q=\"123156\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123156\"]\r\n\r\n\u24d0 260 ft\r\n\u24d1 3825 sq. ft\r\n\r\n[\/hidden-answer]\r\n\r\nThe length of a rectangle is [latex]26[\/latex] inches and the width is [latex]58[\/latex] inches.\r\n\r\nA rectangular room is [latex]15[\/latex] feet wide by [latex]14[\/latex] feet long.\r\n\r\n[reveal-answer q=\"123256\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123256\"]\r\n\r\n\u24d0 58 ft\r\n\u24d1 210 sq. ft\r\n\r\n[\/hidden-answer]\r\n\r\nA driveway is in the shape of a rectangle [latex]20[\/latex] feet wide by [latex]35[\/latex] feet long.\r\n\r\nIn the following exercises, solve.<\/strong>\r\n\r\nFind the length of a rectangle with perimeter [latex]124[\/latex] inches and width [latex]38[\/latex] inches.\r\n\r\n[reveal-answer q=\"123356\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123356\"]\r\n\r\n24 inches\r\n\r\n[\/hidden-answer]\r\n\r\nFind the length of a rectangle with perimeter [latex]20.2[\/latex] yards and width of [latex]7.8[\/latex] yards.\r\n\r\nFind the width of a rectangle with perimeter [latex]92[\/latex] meters and length [latex]19[\/latex] meters.\r\n\r\n[reveal-answer q=\"123556\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123556\"]\r\n\r\n27 meters\r\n\r\n[\/hidden-answer]\r\n\r\nFind the width of a rectangle with perimeter [latex]16.2[\/latex] meters and length [latex]3.2[\/latex] meters.\r\n\r\nThe area of a rectangle is [latex]414[\/latex] square meters. The length is [latex]18[\/latex] meters. What is the width?\r\n\r\n[reveal-answer q=\"123416\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123416\"]\r\n\r\n23 m[\/hidden-answer]\r\n\r\nThe area of a rectangle is [latex]782[\/latex] square centimeters. The width is [latex]17[\/latex] centimeters. What is the length?\r\n\r\nThe length of a rectangle is [latex]9[\/latex] inches more than the width. The perimeter is [latex]46[\/latex] inches. Find the length and the width.\r\n\r\n[reveal-answer q=\"123426\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123426\"]7 in., 16 in.[\/hidden-answer]\r\n\r\nThe width of a rectangle is [latex]8[\/latex] inches more than the length. The perimeter is [latex]52[\/latex] inches. Find the length and the width.\r\n\r\nThe perimeter of a rectangle is [latex]58[\/latex] meters. The width of the rectangle is [latex]5[\/latex] meters less than the length. Find the length and the width of the rectangle.\r\n\r\n[reveal-answer q=\"123451\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123451\"]17 m, 12 m[\/hidden-answer]\r\n\r\nThe perimeter of a rectangle is [latex]62[\/latex] feet. The width is [latex]7[\/latex] feet less than the length. Find the length and the width.\r\n\r\nThe width of the rectangle is [latex]0.7[\/latex] meters less than the length. The perimeter of a rectangle is [latex]52.6[\/latex] meters. Find the dimensions of the rectangle.\r\n\r\n[reveal-answer q=\"123499\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123499\"]13.5 m, 12.8 m[\/hidden-answer]\r\n\r\nThe length of the rectangle is [latex]1.1[\/latex] meters less than the width. The perimeter of a rectangle is [latex]49.4[\/latex] meters. Find the dimensions of the rectangle.\r\n\r\nThe perimeter of a rectangle of [latex]150[\/latex] feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.\r\n\r\n[reveal-answer q=\"123459\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123459\"]25 ft, 50 ft[\/hidden-answer]\r\n\r\nThe length of a rectangle is three times the width. The perimeter is [latex]72[\/latex] feet. Find the length and width of the rectangle.<\/span>\r\n\r\nThe length of a rectangle is [latex]3[\/latex] meters less than twice the width. The perimeter is [latex]36[\/latex] meters. Find the length and width.\r\n\r\n[reveal-answer q=\"123496\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123496\"]7 m, 11 m[\/hidden-answer]\r\n\r\nThe length of a rectangle is [latex]5[\/latex] inches more than twice the width. The perimeter is [latex]34[\/latex] inches. Find the length and width.\r\n\r\nThe width of a rectangular window is [latex]24[\/latex] inches. The area is [latex]624[\/latex] square inches. What is the length?\r\n\r\n[reveal-answer q=\"123476\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123476\"]26 in.[\/hidden-answer]\r\n\r\nThe length of a rectangular poster is [latex]28[\/latex] inches. The area is [latex]1316[\/latex] square inches. What is the width?\r\n\r\nThe area of a rectangular roof is [latex]2310[\/latex] square meters. The length is [latex]42[\/latex] meters. What is the width?\r\n\r\n[reveal-answer q=\"654321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654321\"]55 m[\/hidden-answer]\r\n\r\nThe area of a rectangular tarp is [latex]132[\/latex] square feet. The width is [latex]12[\/latex] feet. What is the length?\r\n\r\nThe perimeter of a rectangular courtyard is [latex]160[\/latex] feet. The length is [latex]10[\/latex] feet more than the width. Find the length and the width.\r\n\r\n[reveal-answer q=\"154321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"154321\"]35 ft, 45 ft[\/hidden-answer]\r\n\r\nThe perimeter of a rectangular painting is [latex]306[\/latex] centimeters. The length is [latex]17[\/latex] centimeters more than the width. Find the length and the width.\r\n\r\nThe width of a rectangular window is [latex]40[\/latex] inches less than the height. The perimeter of the doorway is [latex]224[\/latex] inches. Find the length and the width.\r\n\r\n[reveal-answer q=\"254321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"254321\"]76 in., 36 in.[\/hidden-answer]\r\n\r\nThe width of a rectangular playground is [latex]7[\/latex] meters less than the length. The perimeter of the playground is [latex]46[\/latex] meters. Find the length and the width.\r\n\r\nUse the Properties of Triangles<\/strong>\r\nIn the following exercises, solve using the properties of triangles.<\/strong>\r\n\r\nFind the area of a triangle with base [latex]12[\/latex] inches and height [latex]5[\/latex] inches.\r\n\r\n[reveal-answer q=\"354321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"354321\"]60 sq. in.[\/hidden-answer]\r\n\r\nFind the area of a triangle with base [latex]45[\/latex] centimeters and height [latex]30[\/latex] centimeters.\r\n\r\nFind the area of a triangle with base [latex]8.3[\/latex] meters and height [latex]6.1[\/latex] meters.\r\n\r\n[reveal-answer q=\"754321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"754321\"]25.315 sq. m[\/hidden-answer]\r\n\r\nFind the area of a triangle with base [latex]24.2[\/latex] feet and height [latex]20.5[\/latex] feet.\r\n\r\nA triangular flag has base of [latex]1[\/latex] foot and height of [latex]1.5[\/latex] feet. What is its area?\r\n\r\n[reveal-answer q=\"854321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"854321\"]0.75 sq. ft[\/hidden-answer]\r\n\r\nA triangular window has base of [latex]8[\/latex] feet and height of [latex]6[\/latex] feet. What is its area?\r\n\r\nIf a triangle has sides of [latex]6[\/latex] feet and [latex]9[\/latex] feet and the perimeter is [latex]23[\/latex] feet, how long is the third side?\r\n\r\n[reveal-answer q=\"954321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"954321\"]8 ft[\/hidden-answer]\r\n\r\nIf a triangle has sides of [latex]14[\/latex] centimeters and [latex]18[\/latex] centimeters and the perimeter is [latex]49[\/latex] centimeters, how long is the third side?\r\n\r\nWhat is the base of a triangle with an area of [latex]207[\/latex] square inches and height of [latex]18[\/latex] inches?\r\n\r\n[reveal-answer q=\"614321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"614321\"]23 in.[\/hidden-answer]\r\n\r\nWhat is the height of a triangle with an area of [latex]893[\/latex] square inches and base of [latex]38[\/latex] inches?\r\n\r\nThe perimeter of a triangular reflecting pool is [latex]36[\/latex] yards. The lengths of two sides are [latex]10[\/latex] yards and [latex]15[\/latex] yards. How long is the third side?\r\n\r\n[reveal-answer q=\"624321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"624321\"]11 ft[\/hidden-answer]\r\n\r\nA triangular courtyard has perimeter of [latex]120[\/latex] meters. The lengths of two sides are [latex]30[\/latex] meters and [latex]50[\/latex] meters. How long is the third side?\r\n\r\nAn isosceles triangle has a base of [latex]20[\/latex] centimeters. If the perimeter is [latex]76[\/latex] centimeters, find the length of each of the other sides.\r\n\r\n[reveal-answer q=\"634321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"634321\"]28 cm[\/hidden-answer]\r\n\r\nAn isosceles triangle has a base of [latex]25[\/latex] inches. If the perimeter is [latex]95[\/latex] inches, find the length of each of the other sides.\r\n\r\nFind the length of each side of an equilateral triangle with a perimeter of [latex]51[\/latex] yards.\r\n\r\n[reveal-answer q=\"644321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"644321\"]17 ft[\/hidden-answer]\r\n\r\nFind the length of each side of an equilateral triangle with a perimeter of [latex]54[\/latex] meters.\r\n\r\nThe perimeter of an equilateral triangle is [latex]18[\/latex] meters. Find the length of each side.\r\n\r\n[reveal-answer q=\"664321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"664321\"]6 m[\/hidden-answer]\r\n\r\nThe perimeter of an equilateral triangle is [latex]42[\/latex] miles. Find the length of each side.\r\n\r\nThe perimeter of an isosceles triangle is [latex]42[\/latex] feet. The length of the shortest side is [latex]12[\/latex] feet. Find the length of the other two sides.\r\n\r\n[reveal-answer q=\"674321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"674321\"]15 ft[\/hidden-answer]\r\n\r\nThe perimeter of an isosceles triangle is [latex]83[\/latex] inches. The length of the shortest side is [latex]24[\/latex] inches. Find the length of the other two sides.<\/span>\r\n\r\nA dish is in the shape of an equilateral triangle. Each side is [latex]8[\/latex] inches long. Find the perimeter.\r\n\r\n[reveal-answer q=\"684321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"684321\"]24 in.[\/hidden-answer]\r\n\r\nA floor tile is in the shape of an equilateral triangle. Each side is [latex]1.5[\/latex] feet long. Find the perimeter.\r\n\r\nA road sign in the shape of an isosceles triangle has a base of [latex]36[\/latex] inches. If the perimeter is [latex]91[\/latex] inches, find the length of each of the other sides.\r\n\r\n[reveal-answer q=\"694321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"694321\"]27.5 in.[\/hidden-answer]\r\n\r\nA scarf in the shape of an isosceles triangle has a base of [latex]0.75[\/latex] meters. If the perimeter is [latex]2[\/latex] meters, find the length of each of the other sides.\r\n\r\nThe perimeter of a triangle is [latex]39[\/latex] feet. One side of the triangle is [latex]1[\/latex] foot longer than the second side. The third side is [latex]2[\/latex] feet longer than the second side. Find the length of each side.\r\n\r\n[reveal-answer q=\"651321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"651321\"]12 ft, 13 ft, 14 ft[\/hidden-answer]\r\n\r\nThe perimeter of a triangle is [latex]35[\/latex] feet. One side of the triangle is [latex]5[\/latex] feet longer than the second side. The third side is [latex]3[\/latex] feet longer than the second side. Find the length of each side.\r\n\r\nOne side of a triangle is twice the smallest side. The third side is [latex]5[\/latex] feet more than the shortest side. The perimeter is [latex]17[\/latex] feet. Find the lengths of all three sides.\r\n\r\n[reveal-answer q=\"652321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"652321\"]3 ft, 6 ft, 8 ft[\/hidden-answer]\r\n\r\nOne side of a triangle is three times the smallest side. The third side is [latex]3[\/latex] feet more than the shortest side. The perimeter is [latex]13[\/latex] feet. Find the lengths of all three sides.\r\n\r\nUse the Properties of Trapezoids<\/strong>\r\nIn the following exercises, solve using the properties of trapezoids.<\/strong>\r\n\r\nThe height of a trapezoid is [latex]12[\/latex] feet and the bases are [latex]9[\/latex] and [latex]15[\/latex] feet. What is the area?\r\n\r\n[reveal-answer q=\"654121\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654121\"]144 sq. ft[\/hidden-answer]\r\n\r\nThe height of a trapezoid is [latex]24[\/latex] yards and the bases are [latex]18[\/latex] and [latex]30[\/latex] yards. What is the area?\r\n\r\nFind the area of a trapezoid with a height of [latex]51[\/latex] meters and bases of [latex]43[\/latex] and [latex]67[\/latex] meters.\r\n\r\n[reveal-answer q=\"654221\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654221\"]2805 sq. m[\/hidden-answer]\r\n\r\nFind the area of a trapezoid with a height of [latex]62[\/latex] inches and bases of [latex]58[\/latex] and [latex]75[\/latex] inches.\r\n\r\nThe height of a trapezoid is [latex]15[\/latex] centimeters and the bases are [latex]12.5[\/latex] and [latex]18.3[\/latex] centimeters. What is the area?\r\n\r\n[reveal-answer q=\"654421\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654421\"]231 sq. cm[\/hidden-answer]\r\n\r\nThe height of a trapezoid is [latex]48[\/latex] feet and the bases are [latex]38.6[\/latex] and [latex]60.2[\/latex] feet. What is the area?\r\n\r\nFind the area of a trapezoid with a height of [latex]4.2[\/latex] meters and bases of [latex]8.1[\/latex] and [latex]5.5[\/latex] meters.\r\n\r\n[reveal-answer q=\"654521\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654521\"]28.56 sq. m[\/hidden-answer]\r\n\r\nFind the area of a trapezoid with a height of [latex]32.5[\/latex] centimeters and bases of [latex]54.6[\/latex] and [latex]41.4[\/latex] centimeters.\r\n\r\nLaurel is making a banner shaped like a trapezoid. The height of the banner is [latex]3[\/latex] feet and the bases are [latex]4[\/latex] and [latex]5[\/latex] feet. What is the area of the banner?\r\n\r\n[reveal-answer q=\"654621\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654621\"]13.5 sq. ft[\/hidden-answer]\r\n\r\nNiko wants to tile the floor of his bathroom. The floor is shaped like a trapezoid with width [latex]5[\/latex] feet and lengths [latex]5[\/latex] feet and [latex]8[\/latex] feet. What is the area of the floor?\r\n\r\nTheresa needs a new top for her kitchen counter. The counter is shaped like a trapezoid with width [latex]18.5[\/latex] inches and lengths [latex]62[\/latex] and [latex]50[\/latex] inches. What is the area of the counter?\r\n\r\n[reveal-answer q=\"654721\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654721\"]1036 sq. in.[\/hidden-answer]\r\n\r\nElena is knitting a scarf. The scarf will be shaped like a trapezoid with width [latex]8[\/latex] inches and lengths [latex]48.2[\/latex] inches and [latex]56.2[\/latex] inches. What is the area of the scarf?<\/span>\r\n

Everyday Math<\/h2>\r\nFence<\/strong> Jose just removed the children\u2019s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a [latex]50[\/latex] foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be [latex]10[\/latex] feet. How long can he make the other side if he wants to use the entire roll of fence?\r\n\r\n[reveal-answer q=\"654821\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654821\"]15 ft[\/hidden-answer]\r\n\r\nGardening<\/strong> Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take [latex]48[\/latex] feet of fencing to enclose the garden. Find the length and width of her garden.\r\n\r\nFence<\/strong> Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are [latex]6[\/latex] feet, [latex]8[\/latex] feet, and [latex]10[\/latex] feet. The fence costs [latex]$10[\/latex] per foot. How much will it cost for Christa to fence in her flowerbed?\r\n\r\n[reveal-answer q=\"654921\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654921\"]$24[\/hidden-answer]\r\n\r\nPainting<\/strong> Caleb wants to paint one wall of his attic. The wall is shaped like a trapezoid with height [latex]8[\/latex] feet and bases [latex]20[\/latex] feet and [latex]12[\/latex] feet. The cost of the painting one square foot of wall is about [latex]$0.05[\/latex]. About how much will it cost for Caleb to paint the attic wall?\r\n\r\n\"A\r\n

Writing Exercises<\/h2>\r\nIf you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.\r\n\r\nAnswers will vary.\r\n\r\nIf you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.\r\n\r\nLook at the two figures.\r\n\r\n\"A\r\n\u24d0 Which figure looks like it has the larger area? Which looks like it has the larger perimeter?\r\n\u24d1 Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?\r\n\r\nAnswers will vary.\r\n\r\nThe length of a rectangle is [latex]5[\/latex] feet more than the width. The area is [latex]50[\/latex] square feet. Find the length and the width.\r\n\u24d0 Write the equation you would use to solve the problem.\r\n\u24d1 Why can\u2019t you solve this equation with the methods you learned in the previous chapter?\r\n

Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\".\"\r\n\u24d1 On a scale of 1\u201310, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?\r\n

<\/h2>\r\n

Solve Geometry Applications: Circles and Irregular Figures<\/h2>\r\nUse Properties of Circles<\/strong>\r\nIn the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.<\/strong>\r\n\r\nA circular mosaic has radius [latex]3[\/latex] meters. Find the \u24d0 circumference \u24d1 area of the mosaic.\r\n\r\n[reveal-answer q=\"654021\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654021\"]\u24d0 18.84 m\r\n\u24d1 28.26 sq. m[\/hidden-answer]\r\n\r\nA circular fountain has radius [latex]8[\/latex] feet. Find the\u00a0<\/span>\u24d0 circumference \u24d1 area of the fountain.\r\n\r\nFind the diameter of a circle with circumference [latex]150.72[\/latex] inches.\r\n\r\n[reveal-answer q=\"654311\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654311\"]48 in.[\/hidden-answer]\r\n\r\nFind the radius of a circle with circumference [latex]345.4[\/latex] centimeters\r\n\r\nFind the Area of Irregular Figures<\/strong>\r\nIn the following exercises, find the area of each shaded region.<\/strong>\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"654331\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654331\"]30 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"654341\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654341\"]300 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"654351\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654351\"]199.25 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n

Solve Geometry Applications: Volume and Surface Area<\/h2>\r\nFind Volume and Surface Area of Rectangular Solids<\/strong>\r\nIn the following exercises, find the \u24d0 volume \u24d1 surface area of the rectangular solid.<\/strong>\r\n\r\na rectangular solid with length [latex]14[\/latex] centimeters, width [latex]4.5[\/latex] centimeters, and height [latex]10[\/latex] centimeters\r\n\r\n[reveal-answer q=\"654361\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654361\"]\u24d0 630 cu. cm\r\n\u24d1 496 sq. cm[\/hidden-answer]\r\n\r\na cube with sides that are [latex]3[\/latex] feet long\r\n\r\na cube of tofu with sides [latex]2.5[\/latex] inches\r\n\r\n[reveal-answer q=\"654371\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654371\"]\u24d0 15.625 cu. in.\r\n\u24d1 37.5 sq. in.[\/hidden-answer]\r\n\r\na rectangular carton with length [latex]32[\/latex] inches, width [latex]18[\/latex] inches, and height [latex]10[\/latex] inches\r\n\r\nFind Volume and Surface Area of Spheres<\/strong>\r\nIn the following exercises, find the \u24d0 volume \u24d1 surface area of the sphere.<\/strong>\r\n\r\na sphere with radius [latex]4[\/latex] yards\r\n\r\n[reveal-answer q=\"654381\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654381\"]\u24d0 267.95 cu. yd.\r\n\u24d1 200.96 sq. yd.[\/hidden-answer]\r\n\r\na sphere with radius [latex]12[\/latex] meters\r\n\r\na baseball with radius [latex]1.45[\/latex] inches\r\n\r\n[reveal-answer q=\"654391\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654391\"]\u24d0 12.76 cu. in.\r\n\u24d1 26.41 sq. in.[\/hidden-answer]\r\n\r\na soccer ball with radius [latex]22[\/latex] centimeters\r\n\r\nFind Volume and Surface Area of Cylinders<\/strong>\r\nIn the following exercises, find the \u24d0 volume \u24d1 surface area of the cylinder.<\/strong>\r\n\r\na cylinder with radius [latex]2[\/latex] yards and height [latex]6[\/latex] yards\r\n\r\n[reveal-answer q=\"654301\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654301\"]\u24d0 75.36 cu. yd.\r\n\u24d1 100.48 sq. yd.[\/hidden-answer]\r\n\r\na cylinder with diameter [latex]18[\/latex] inches and height [latex]40[\/latex] inches\r\n\r\na juice can with diameter [latex]8[\/latex] centimeters and height [latex]15[\/latex] centimeters\r\n\r\n[reveal-answer q=\"654322\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654322\"]\u24d0 753.6 cu. cm\r\n\u24d1 477.28 sq. cm[\/hidden-answer]\r\n\r\na cylindrical pylon with diameter [latex]0.8[\/latex] feet and height [latex]2.5[\/latex] feet\r\n\r\nFind Volume of Cones<\/strong>\r\nIn the following exercises, find the volume of the cone.<\/strong>\r\n\r\na cone with height [latex]5[\/latex] meters and radius [latex]1[\/latex] meter\r\n\r\n[reveal-answer q=\"654323\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654323\"]5.233 cu. m[\/hidden-answer]\r\n\r\na cone with height [latex]24[\/latex] feet and radius [latex]8[\/latex] feet\r\n\r\na cone-shaped water cup with diameter [latex]2.6[\/latex] inches and height [latex]2.6[\/latex] inches\r\n\r\n[reveal-answer q=\"654324\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654324\"]4.599 cu. in.[\/hidden-answer]\r\n\r\na cone-shaped pile of gravel with diameter [latex]6[\/latex] yards and height [latex]5[\/latex] yards\r\n

Mixed Practice<\/h2>\r\nFind the complement of a [latex]{52^\\circ }[\/latex] angle.\r\n\r\n[reveal-answer q=\"654325\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654325\"]38\u00b0[\/hidden-answer]\r\n\r\nThe measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is [latex]14[\/latex] more than the measure of the smallest angle. Find the measures of all three angles.\r\n\r\nThe perimeter of an equilateral triangle is [latex]145[\/latex] feet. Find the length of each side.\r\n\r\n[reveal-answer q=\"654326\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654326\"]48.3[\/hidden-answer]\r\n\r\n[latex]\\Delta ABC[\/latex] is similar to [latex]\\Delta XYZ[\/latex]. Find the length of side [latex]c[\/latex].\r\n\r\n\"Two\r\n\r\nFind the length of the missing side. Round to the nearest tenth, if necessary.\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"654327\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654327\"]10[\/hidden-answer]\r\n\r\nFind the length of the missing side. Round to the nearest tenth, if necessary.\r\n\r\n\"A\r\n\r\nA baseball diamond is shaped like a square with sides [latex]90[\/latex] feet long. How far is it from home plate to second base, as shown?\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"654328\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654328\"]127.3 ft[\/hidden-answer]\r\n\r\nThe length of a rectangle is [latex]2[\/latex] feet more than five times the width. The perimeter is [latex]40[\/latex] feet. Find the dimensions of the rectangle.\r\n\r\nA triangular poster has base [latex]80[\/latex] centimeters and height [latex]55[\/latex] centimeters. Find the area of the poster.\r\n\r\n[reveal-answer q=\"654329\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654329\"]2200 square centimeters[\/hidden-answer]\r\n\r\nA trapezoid has height [latex]14[\/latex] inches and bases [latex]20[\/latex] inches and [latex]23[\/latex] inches. Find the area of the trapezoid.\r\n\r\nA circular pool has diameter [latex]90[\/latex] inches. What is its circumference? Round to the nearest tenth.<\/em>\r\n\r\n[reveal-answer q=\"654320\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654320\"]282.6 inches[\/hidden-answer]\r\n\r\nFind the area of the shaded region. Round to the nearest tenth.\r\n\r\n\"A\r\n\r\nFind the volume of a rectangular room with width [latex]12[\/latex] feet, length [latex]15[\/latex] feet, and height [latex]8[\/latex] feet.\r\n\r\n[reveal-answer q=\"114321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"114321\"]1440[\/hidden-answer]\r\n\r\nA coffee can is shaped like a cylinder with height [latex]7[\/latex] inches and radius [latex]5[\/latex] inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth.\r\n\r\nA traffic cone has height [latex]75[\/latex] centimeters. The radius of the base is [latex]20[\/latex] centimeters. Find the volume of the cone. Round to the nearest tenth.\r\n\r\n[reveal-answer q=\"224321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"224321\"]31,400 cubic inches[\/hidden-answer]\r\n\r\nSolve the formula [latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex] for [latex]h\\text{:}[\/latex] \u24d0 when [latex]A=1716[\/latex] and [latex]b=66[\/latex] \u24d1 in general.\r\n\r\n[reveal-answer q=\"334321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"334321\"]\u24d0 [latex]\\text{height}=52[\/latex]\r\n\u24d1 [latex]h=\\Large\\frac{2A}{b}[\/latex][\/hidden-answer]\r\n\r\nSolve [latex]x+5y=14[\/latex] for [latex]y[\/latex].\r\n

Practice Makes Perfect<\/h2>\r\nUse the Properties of Circles<\/strong>\r\nIn the following exercises, solve using the properties of circles.\r\n\r\nThe lid of a paint bucket is a circle with radius [latex]7[\/latex] inches. Find the \u24d0 circumference and \u24d1 area of the lid.\r\n\r\n[reveal-answer q=\"444321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"444321\"]\u24d0 43.96 in.\r\n\u24d1 153.86 sq. in.[\/hidden-answer]\r\n\r\nAn extra-large pizza is a circle with radius [latex]8[\/latex] inches. Find the \u24d0 circumference and \u24d1 area of the pizza.\r\n\r\nA farm sprinkler spreads water in a circle with radius of [latex]8.5[\/latex] feet. Find the \u24d0 circumference and \u24d1 area of the watered circle.\r\n\r\n[reveal-answer q=\"774321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"774321\"]\u24d0 53.38 ft\r\n\u24d1 226.865 sq. ft[\/hidden-answer]\r\n\r\nA circular rug has radius of [latex]3.5[\/latex] feet. Find the \u24d0 circumference and \u24d1 area of the rug.\r\n\r\nA reflecting pool is in the shape of a circle with diameter of [latex]20[\/latex] feet. What is the circumference of the pool?\r\n\r\n[reveal-answer q=\"884321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"884321\"]62.8 ft[\/hidden-answer]\r\n\r\nA turntable is a circle with diameter of [latex]10[\/latex] inches. What is the circumference of the turntable?\r\n\r\nA circular saw has a diameter of [latex]12[\/latex] inches. What is the circumference of the saw?\r\n\r\n[reveal-answer q=\"994321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"994321\"]37.68 in.[\/hidden-answer]\r\n\r\nA round coin has a diameter of [latex]3[\/latex] centimeters. What is the circumference of the coin?\r\n\r\nA barbecue grill is a circle with a diameter of [latex]2.2[\/latex] feet. What is the circumference of the grill?\r\n\r\n[reveal-answer q=\"004321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"004321\"]6.908 ft[\/hidden-answer]\r\n\r\nThe top of a pie tin is a circle with a diameter of [latex]9.5[\/latex] inches. What is the circumference of the top?\r\n\r\nA circle has a circumference of [latex]163.28[\/latex] inches. Find the diameter.\r\n\r\n[reveal-answer q=\"611321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"611321\"]52 in.[\/hidden-answer]\r\n\r\nA circle has a circumference of [latex]59.66[\/latex] feet. Find the diameter.\r\n\r\nA circle has a circumference of [latex]17.27[\/latex] meters. Find the diameter.\r\n\r\n[reveal-answer q=\"622321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"622321\"]5.5 m[\/hidden-answer]\r\n\r\nA circle has a circumference of [latex]80.07[\/latex] centimeters. Find the diameter.\r\n\r\nIn the following exercises, find the radius of the circle with given circumference.<\/strong>\r\n\r\nA circle has a circumference of [latex]150.72[\/latex] feet.\r\n\r\n[reveal-answer q=\"633321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"633321\"]24 ft[\/hidden-answer]\r\n\r\nA circle has a circumference of [latex]251.2[\/latex] centimeters.\r\n\r\nA circle has a circumference of [latex]40.82[\/latex] miles.\r\n\r\n[reveal-answer q=\"666321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"666321\"]6.5 mi[\/hidden-answer]\r\n\r\nA circle has a circumference of [latex]78.5[\/latex] inches.\r\n\r\nFind the Area of Irregular Figures<\/strong>\r\nIn the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"677321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"677321\"]16 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"688321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"688321\"]30 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"699321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"699321\"]57.5 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"Two\r\n\r\n[reveal-answer q=\"600321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"600321\"]12 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"651121\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"651121\"]67.5 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"652221\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"652221\"]89 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"655521\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"655521\"]44.81 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"656621\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"656621\"]41.12 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"657721\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"657721\"]35.13 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"658821\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"658821\"]95.625 sq. units[\/hidden-answer]\r\n\r\n\"A\r\n\r\nIn the following exercises, solve.<\/strong>\r\n\r\nA city park covers one block plus parts of four more blocks, as shown. The block is a square with sides [latex]250[\/latex] feet long, and the triangles are isosceles right triangles. Find the area of the park.\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"659921\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"659921\"]187,500 sq. ft[\/hidden-answer]\r\n\r\nA gift box will be made from a rectangular piece of cardboard measuring [latex]12[\/latex] inches by [latex]20[\/latex] inches, with squares cut out of the corners of the sides, as shown. The sides of the squares are [latex]3[\/latex] inches. Find the area of the cardboard after the corners are cut out.\r\n\r\n\"A\r\n\r\nPerry needs to put in a new lawn. His lot is a rectangle with a length of [latex]120[\/latex] feet and a width of [latex]100[\/latex] feet. The house is rectangular and measures [latex]50[\/latex] feet by [latex]40[\/latex] feet. His driveway is rectangular and measures [latex]20[\/latex] feet by [latex]30[\/latex] feet, as shown. Find the area of Perry\u2019s lawn.\r\n\r\n\"A\r\n\r\n[reveal-answer q=\"650021\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"650021\"]9400 sq. ft[\/hidden-answer]\r\n\r\nDenise is planning to put a deck in her back yard. The deck will be a [latex]\\text{20-ft}[\/latex] by [latex]\\text{12-ft}[\/latex] rectangle with a semicircle of diameter [latex]6[\/latex] feet, as shown below. Find the area of the deck.<\/span>\r\n\r\n\"A\r\n

Everyday Math<\/h2>\r\nArea of a Tabletop<\/strong> Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a [latex]\\text{1-ft}[\/latex] by [latex]\\text{3-ft}[\/latex] rectangle with a semicircle at each end, as shown. \u24d0 Find the area of the table with one leaf up. \u24d1 Find the area of the table with both leaves up.\r\n\r\n\"An\r\n\r\n[reveal-answer q=\"654111\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654111\"]\u24d0 6.5325 sq. ft\r\n\u24d1 10.065 sq. ft[\/hidden-answer]\r\n\r\nPainting<\/strong> Leora wants to paint the nursery in her house. The nursery is an [latex]\\text{8-ft}[\/latex] by [latex]\\text{10-ft}[\/latex] rectangle, and the ceiling is [latex]8[\/latex] feet tall. There is a [latex]\\text{3-ft}[\/latex] by [latex]\\text{6.5-ft}[\/latex] door on one wall, a [latex]\\text{3-ft}[\/latex] by [latex]\\text{6.5-ft}[\/latex] closet door on another wall, and one [latex]\\text{4-ft}[\/latex] by [latex]\\text{3.5-ft}[\/latex] window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?\r\n

Writing Exercises<\/h2>\r\nDescribe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.\r\n\r\n\"A\r\n\r\nAnswers will vary.\r\n\r\nA circle has a diameter of [latex]14[\/latex] feet. Find the area of the circle \u24d0 using [latex]3.14[\/latex] for [latex]\\pi [\/latex] \u24d1 using [latex]\\Large\\frac{22}{7}[\/latex] for [latex]\\text{\\pi }[\/latex]. \u24d2 Which calculation to do prefer? Why?\r\n

Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\".\"\r\n\u24d1 After looking at the checklist, do you think you are well prepared for the next section? Why or why not?\r\n

<\/h2>\r\n

Practice Makes Perfect<\/h2>\r\nFind Volume and Surface Area of Rectangular Solids<\/strong>\r\nIn the following exercises, find \u24d0 the volume and \u24d1 the surface area of the rectangular solid with the given dimensions.<\/strong>\r\n\r\nlength [latex]2[\/latex] meters, width [latex]1.5[\/latex] meters, height [latex]3[\/latex] meters\r\n\r\n[reveal-answer q=\"654441\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654441\"]\u24d0 9 cu. m\r\n\u24d1 27 sq. m[\/hidden-answer]\r\n\r\nlength [latex]5[\/latex] feet, width [latex]8[\/latex] feet, height [latex]2.5[\/latex] feet\r\n\r\nlength [latex]3.5[\/latex] yards, width [latex]2.1[\/latex] yards, height [latex]2.4[\/latex] yards\r\n\r\n[reveal-answer q=\"654551\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654551\"]\u24d0 17.64 cu. yd.\r\n\u24d1 41.58 sq. yd.[\/hidden-answer]\r\n\r\nlength [latex]8.8[\/latex] centimeters, width [latex]6.5[\/latex] centimeters, height [latex]4.2[\/latex] centimeters\r\n\r\nIn the following exercises, solve.<\/strong>\r\n\r\nMoving van<\/strong> A rectangular moving van has length [latex]16[\/latex] feet, width [latex]8[\/latex] feet, and height [latex]8[\/latex] feet. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"654661\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654661\"]\u24d0 1,024 cu. ft\r\n\u24d1 640 sq. ft[\/hidden-answer]\r\n\r\nGift box<\/strong> A rectangular gift box has length [latex]26[\/latex] inches, width [latex]16[\/latex] inches, and height [latex]4[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nCarton<\/strong> A rectangular carton has length\r\n[latex]21.3[\/latex] cm, width [latex]24.2[\/latex] cm, and height [latex]6.5[\/latex] cm. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"654771\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654771\"]\u24d0 3,350.49 cu. cm\r\n\u24d1 1,622.42 sq. cm[\/hidden-answer]\r\n\r\nShipping container<\/strong> A rectangular shipping container has length [latex]22.8[\/latex] feet, width [latex]8.5[\/latex] feet, and height [latex]8.2[\/latex] feet. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nIn the following exercises, find \u24d0 the volume and \u24d1 the surface area of the cube with the given side length.<\/strong>\r\n\r\n[latex]5[\/latex] centimeters\r\n\r\n[reveal-answer q=\"654881\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654881\"]\u24d0 125 cu. cm\r\n\u24d1 150 sq. cm[\/hidden-answer]\r\n\r\n[latex]6[\/latex] inches\r\n\r\n[latex]10.4[\/latex] feet\r\n\r\n[reveal-answer q=\"654991\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654991\"]\u24d0 1124.864 cu. ft.\r\n\u24d1 648.96 sq. ft[\/hidden-answer]\r\n\r\n[latex]12.5[\/latex] meters\r\n\r\nIn the following exercises, solve.<\/strong>\r\n\r\nScience center<\/strong> Each side of the cube at the Discovery Science Center in Santa Ana is [latex]64[\/latex] feet long. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"654001\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654001\"]\u24d0 262,144 cu. ft\r\n\u24d1 24,576 sq. ft[\/hidden-answer]\r\n\r\nMuseum<\/strong> A cube-shaped museum has sides [latex]45[\/latex] meters long. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nBase of statue<\/strong> The base of a statue is a cube with sides [latex]2.8[\/latex] meters long. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"654333\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654333\"]\u24d0 21.952 cu. m\r\n\u24d1 47.04 sq. m[\/hidden-answer]\r\n\r\nTissue box<\/strong> A box of tissues is a cube with sides 4.5 inches long. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nFind the Volume and Surface Area of Spheres<\/strong>\r\n\r\nIn the following exercises, find \u24d0 the volume and \u24d1 the surface area of the sphere with the given radius. Round answers to the nearest hundredth.<\/strong>\r\n\r\n[latex]3[\/latex] centimeters\r\n\r\n[reveal-answer q=\"654344\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654344\"]\u24d0 113.04 cu. cm\r\n\u24d1 113.04 sq. cm[\/hidden-answer]\r\n\r\n[latex]9[\/latex] inches\r\n\r\n[latex]7.5[\/latex] feet\r\n\r\n[reveal-answer q=\"654355\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654355\"]\u24d0 1,766.25 cu. ft\r\n\u24d1 706.5 sq. ft [\/hidden-answer]\r\n\r\n[latex]2.1[\/latex] yards\r\n\r\nIn the following exercises, solve. Round answers to the nearest hundredth.<\/strong>\r\n\r\nExercise ball<\/strong> An exercise ball has a radius of [latex]15[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"654366\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654366\"]\u24d0 14,130 cu. in.\r\n\u24d1 2,826 sq. in.[\/hidden-answer]\r\n\r\nBalloon ride<\/strong> The Great Park Balloon is a big orange sphere with a radius of [latex]36[\/latex] feet . Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nGolf ball<\/strong> A golf ball has a radius of [latex]4.5[\/latex] centimeters. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"654377\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654377\"]\u24d0 381.51 cu. cm\r\n\u24d1 254.34 sq. cm[\/hidden-answer]\r\n\r\nBaseball<\/strong> A baseball has a radius of [latex]2.9[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nFind the Volume and Surface Area of a Cylinder<\/strong>\r\nIn the following exercises, find \u24d0 the volume and \u24d1 the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.<\/strong>\r\n\r\nradius [latex]3[\/latex] feet, height [latex]9[\/latex] feet\r\n\r\n[reveal-answer q=\"987654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987654\"]\u24d0 254.34 cu. ft\r\n\u24d1 226.08 sq. ft[\/hidden-answer]\r\n\r\nradius [latex]5[\/latex] centimeters, height [latex]15[\/latex] centimeters\r\n\r\nradius [latex]1.5[\/latex] meters, height [latex]4.2[\/latex] meters\r\n\r\n[reveal-answer q=\"187654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"187654\"]\u24d0 29.673 cu. m\r\n\u24d1 53.694 sq. m[\/hidden-answer]\r\n\r\nradius [latex]1.3[\/latex] yards, height [latex]2.8[\/latex] yards\r\n\r\nIn the following exercises, solve. Round answers to the nearest hundredth.<\/strong>\r\n\r\nCoffee can<\/strong> A can of coffee has a radius of [latex]5[\/latex] cm and a height of [latex]13[\/latex] cm. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"287654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"287654\"]\u24d0 1,020.5 cu. cm\r\n\u24d1 565.2 sq. cm[\/hidden-answer]\r\n\r\nSnack pack<\/strong> A snack pack of cookies is shaped like a cylinder with radius [latex]4[\/latex] cm and height [latex]3[\/latex] cm. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nBarber shop pole<\/strong> A cylindrical barber shop pole has a diameter of [latex]6[\/latex] inches and height of [latex]24[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\n[reveal-answer q=\"387654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"387654\"]\u24d0 678.24 cu. in.\r\n\u24d1 508.68 sq. in.[\/hidden-answer]\r\n\r\nArchitecture<\/strong> A cylindrical column has a diameter of [latex]8[\/latex] feet and a height of [latex]28[\/latex] feet. Find its \u24d0 volume and \u24d1 surface area.\r\n\r\nFind the Volume of Cones<\/strong>\r\nIn the following exercises, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.<\/strong>\r\n\r\nheight [latex]9[\/latex] feet and radius [latex]2[\/latex] feet\r\n\r\n[reveal-answer q=\"487654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"487654\"]37.68 cu. ft[\/hidden-answer]\r\n\r\nheight [latex]8[\/latex] inches and radius [latex]6[\/latex] inches\r\n\r\nheight [latex]12.4[\/latex] centimeters and radius [latex]5[\/latex] cm\r\n\r\n[reveal-answer q=\"587654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"587654\"]324.47 cu. cm[\/hidden-answer]\r\n\r\nheight [latex]15.2[\/latex] meters and radius [latex]4[\/latex] meters\r\n\r\nIn the following exercises, solve. Round answers to the nearest hundredth.<\/strong>\r\n\r\nTeepee<\/strong> What is the volume of a cone-shaped tee-pee tent that is [latex]10[\/latex] feet tall and [latex]10[\/latex] feet across at the base?\r\n\r\n[reveal-answer q=\"687654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"687654\"]261.67 cu. ft[\/hidden-answer]\r\n\r\nPopcorn cup<\/strong> What is the volume of a cone-shaped popcorn cup that is [latex]8[\/latex] inches tall and [latex]6[\/latex] inches across at the base?\r\n\r\nSilo<\/strong> What is the volume of a cone-shaped silo that is [latex]50[\/latex] feet tall and [latex]70[\/latex] feet across at the base?\r\n\r\n[reveal-answer q=\"787654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"787654\"]64,108.33 cu. ft[\/hidden-answer]\r\n\r\nSand pile<\/strong> What is the volume of a cone-shaped pile of sand that is [latex]12[\/latex] meters tall and [latex]30[\/latex] meters across at the base?\r\n

Everyday Math<\/h2>\r\nStreet light post<\/strong> The post of a street light is shaped like a truncated cone, as shown in the picture below. It is a large cone minus a smaller top cone. The large cone is [latex]30[\/latex] feet tall with base radius [latex]1[\/latex] foot. The smaller cone is [latex]10[\/latex] feet tall with base radius of [latex]0.5[\/latex] feet. To the nearest tenth,\r\n\u24d0 find the volume of the large cone.\r\n\u24d1 find the volume of the small cone.\r\n\u24d2 find the volume of the post by subtracting the volume of the small cone from the volume of the large cone.\r\n\r\n\"An\r\n\r\n[reveal-answer q=\"887654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"887654\"]\u24d0 31.4 cu. ft\r\n\u24d1 2.6 cu. ft\r\n\u24d2 28.8 cu. ft[\/hidden-answer]\r\n\r\nIce cream cones<\/strong> A regular ice cream cone is 4 inches tall and has a diameter of [latex]2.5[\/latex] inches. A waffle cone is [latex]7[\/latex] inches tall and has a diameter of [latex]3.25[\/latex] inches. To the nearest hundredth,\r\n\u24d0 find the volume of the regular ice cream cone.\r\n\u24d1 find the volume of the waffle cone.\r\n\u24d2 how much more ice cream fits in the waffle cone compared to the regular cone?\r\n

Writing Exercises<\/h2>\r\nThe formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape.\r\n\r\nAnswers will vary.\r\n\r\nWhich has a larger volume, a cube of sides of [latex]8[\/latex] feet or a sphere with a diameter of [latex]8[\/latex] feet? Explain your reasoning.\r\n

Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\".\"\r\n\u24d1 After reviewing this checklist, what will you do to become confident for all objectives?\r\n

<\/h2>\r\n

Practice Makes Perfect<\/h2>\r\nMake Unit Conversions in the U.S. System<\/strong>\r\nIn the following exercises, convert the units.<\/strong>\r\n\r\nA park bench is [latex]6[\/latex] feet long. Convert the length to inches.\r\n\r\nA floor tile is [latex]2[\/latex] feet wide. Convert the width to inches.\r\n\r\n[reveal-answer q=\"087654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"087654\"]24 inches[\/hidden-answer]\r\n\r\nA ribbon is [latex]18[\/latex] inches long. Convert the length to feet.\r\n\r\nCarson is [latex]45[\/latex] inches tall. Convert his height to feet.\r\n\r\n[reveal-answer q=\"917654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"917654\"]3.75 feet[\/hidden-answer]\r\n\r\nJon is [latex]6[\/latex] feet [latex]4[\/latex] inches tall. Convert his height to inches.\r\n\r\nFaye is [latex]4[\/latex] feet [latex]10[\/latex] inches tall. Convert her height to inches.\r\n\r\n[reveal-answer q=\"927654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"927654\"]58 inches[\/hidden-answer]\r\n\r\nA football field is [latex]160[\/latex] feet wide. Convert the width to yards.\r\n\r\nOn a baseball diamond, the distance from home plate to first base is [latex]30[\/latex] yards. Convert the distance to feet.\r\n\r\n[reveal-answer q=\"937654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"937654\"]90 feet[\/hidden-answer]\r\n\r\nUlises lives [latex]1.5[\/latex] miles from school. Convert the distance to feet.\r\n\r\nDenver, Colorado, is [latex]5,183[\/latex] feet above sea level. Convert the height to miles.\r\n\r\n[reveal-answer q=\"947654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"947654\"]0.98 miles[\/hidden-answer]\r\n\r\nA killer whale weighs [latex]4.6[\/latex] tons. Convert the weight to pounds.\r\n\r\nBlue whales can weigh as much as [latex]150[\/latex] tons. Convert the weight to pounds.\r\n\r\n[reveal-answer q=\"957654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"957654\"]300,000 pounds[\/hidden-answer]\r\n\r\nAn empty bus weighs [latex]35,000[\/latex] pounds. Convert the weight to tons.\r\n\r\nAt take-off, an airplane weighs [latex]220,000[\/latex] pounds. Convert the weight to tons.\r\n\r\n[reveal-answer q=\"967654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"967654\"]110 tons[\/hidden-answer]\r\n\r\nThe voyage of the Mayflower<\/em> took [latex]2[\/latex] months and [latex]5[\/latex] days. Convert the time to days.\r\n\r\nLynn\u2019s cruise lasted [latex]6[\/latex] days and [latex]18[\/latex] hours. Convert the time to hours.\r\n\r\n[reveal-answer q=\"977654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"977654\"]162 hours[\/hidden-answer]\r\n\r\nRocco waited [latex]1\\Large\\frac{1}{2}[\/latex] hours for his appointment. Convert the time to seconds.\r\n\r\nMisty\u2019s surgery lasted [latex]2\\Large\\frac{1}{4}[\/latex] hours. Convert the time to seconds.\r\n\r\n[reveal-answer q=\"997654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"997654\"]8100 seconds[\/hidden-answer]\r\n\r\nHow many teaspoons are in a pint?\r\n\r\nHow many tablespoons are in a gallon?\r\n\r\n[reveal-answer q=\"907654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"907654\"]256 tablespoons[\/hidden-answer]\r\n\r\nJJ\u2019s cat, Posy, weighs [latex]14[\/latex] pounds. Convert her weight to ounces.\r\n\r\nApril\u2019s dog, Beans, weighs [latex]8[\/latex] pounds. Convert his weight to ounces.\r\n\r\n[reveal-answer q=\"981654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"981654\"]128 ounces[\/hidden-answer]\r\n\r\nBaby Preston weighed [latex]7[\/latex] pounds [latex]3[\/latex] ounces at birth. Convert his weight to ounces.\r\n\r\nBaby Audrey weighed [latex]6[\/latex] pounds [latex]15[\/latex] ounces at birth. Convert her weight to ounces.\r\n\r\n[reveal-answer q=\"982654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"982654\"]111 ounces[\/hidden-answer]\r\n\r\nCrista will serve [latex]20[\/latex] cups of juice at her son\u2019s party. Convert the volume to gallons.\r\n\r\nLance needs [latex]500[\/latex] cups of water for the runners in a race. Convert the volume to gallons.\r\n\r\n[reveal-answer q=\"983654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"983654\"]31.25 gallons[\/hidden-answer]\r\n\r\nUse Mixed Units of Measurement in the U.S. System<\/strong>\r\nIn the following exercises, solve and write your answer in mixed units.<\/strong>\r\n\r\nEli caught three fish. The weights of the fish were [latex]2[\/latex] pounds [latex]4[\/latex] ounces, [latex]1[\/latex] pound [latex]11[\/latex] ounces, and [latex]4[\/latex] pounds [latex]14[\/latex] ounces. What was the total weight of the three fish?\r\n\r\nJudy bought [latex]1[\/latex] pound [latex]6[\/latex] ounces of almonds, [latex]2[\/latex] pounds [latex]3[\/latex] ounces of walnuts, and [latex]8[\/latex] ounces of cashews. What was the total weight of the nuts?\r\n\r\n[reveal-answer q=\"984654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"984654\"]4 lbs. 1 oz.[\/hidden-answer]\r\n\r\nOne day Anya kept track of the number of minutes she spent driving. She recorded trips of [latex]45,10,8,65,20,\\text{and 35 minutes.}[\/latex] How much time (in hours and minutes) did Anya spend driving?\r\n\r\nLast year Eric went on [latex]6[\/latex] business trips. The number of days of each was [latex]5,2,8,12,6,\\text{and 3.}[\/latex] How much time (in weeks and days) did Eric spend on business trips last year?\r\n\r\n[reveal-answer q=\"985654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"985654\"]5 weeks and 1 day[\/hidden-answer]\r\n\r\nRenee attached a [latex]\\text{6-foot - 6-inch}[\/latex] extension cord to her computer\u2019s [latex]\\text{3-foot - 8-inch}[\/latex] power cord. What was the total length of the cords?\r\n\r\nFawzi\u2019s SUV is [latex]6[\/latex] feet [latex]4[\/latex] inches tall. If he puts a [latex]\\text{2-foot - 10-inch}[\/latex] box on top of his SUV, what is the total height of the SUV and the box?\r\n\r\n[reveal-answer q=\"986654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"986654\"]9 ft 2 in[\/hidden-answer]\r\n\r\nLeilani wants to make [latex]8[\/latex] placemats. For each placemat she needs [latex]18[\/latex] inches of fabric. How many yards of fabric will she need for the [latex]8[\/latex] placemats?\r\n\r\nMireille needs to cut [latex]24[\/latex] inches of ribbon for each of the [latex]12[\/latex] girls in her dance class. How many yards of ribbon will she need altogether?\r\n\r\n[reveal-answer q=\"988654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"988654\"]8 yards[\/hidden-answer]\r\n\r\nMake Unit Conversions in the Metric System<\/strong>\r\nIn the following exercises, convert the units.<\/strong>\r\n\r\nGhalib ran [latex]5[\/latex] kilometers. Convert the length to meters.\r\n\r\nKitaka hiked [latex]8[\/latex] kilometers. Convert the length to meters.\r\n\r\n[reveal-answer q=\"989654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"989654\"]8000 meters[\/hidden-answer]\r\n\r\nEstrella is [latex]1.55[\/latex] meters tall. Convert her height to centimeters.\r\n\r\nThe width of the wading pool is [latex]2.45[\/latex] meters. Convert the width to centimeters.\r\n\r\n[reveal-answer q=\"980654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"980654\"]245 centimeters[\/hidden-answer]\r\n\r\nMount Whitney is [latex]3,072[\/latex] meters tall. Convert the height to kilometers.\r\n\r\nThe depth of the Mariana Trench is [latex]10,911[\/latex] meters. Convert the depth to kilometers.\r\n\r\n[reveal-answer q=\"987154\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987154\"]10.911 kilometers[\/hidden-answer]\r\n\r\nJune\u2019s multivitamin contains [latex]1,500[\/latex] milligrams of calcium. Convert this to grams.\r\n\r\nA typical ruby-throated hummingbird weights [latex]3[\/latex] grams. Convert this to milligrams.\r\n\r\n[reveal-answer q=\"987254\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987254\"]3000 milligrams[\/hidden-answer]\r\n\r\nOne stick of butter contains [latex]91.6[\/latex] grams of fat. Convert this to milligrams.\r\n\r\nOne serving of gourmet ice cream has [latex]25[\/latex] grams of fat. Convert this to milligrams.\r\n\r\n[reveal-answer q=\"987354\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987354\"]25,000 milligrams[\/hidden-answer]\r\n\r\nThe maximum mass of an airmail letter is [latex]2[\/latex] kilograms. Convert this to grams.\r\n\r\nDimitri\u2019s daughter weighed [latex]3.8[\/latex] kilograms at birth. Convert this to grams.\r\n\r\n[reveal-answer q=\"987454\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987454\"]3800 grams[\/hidden-answer]\r\n\r\nA bottle of wine contained [latex]750[\/latex] milliliters. Convert this to liters.\r\n\r\nA bottle of medicine contained [latex]300[\/latex] milliliters. Convert this to liters.\r\n\r\n[reveal-answer q=\"987554\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987554\"]0.3 liters[\/hidden-answer]\r\n\r\nUse Mixed Units of Measurement in the Metric System<\/strong>\r\nIn the following exercises, solve and write your answer in mixed units.<\/strong>\r\n\r\nMatthias is [latex]1.8[\/latex] meters tall. His son is [latex]89[\/latex] centimeters tall. How much taller, in centimeters, is Matthias than his son?\r\n\r\nStavros is [latex]1.6[\/latex] meters tall. His sister is [latex]95[\/latex] centimeters tall. How much taller, in centimeters, is Stavros than his sister?\r\n\r\n[reveal-answer q=\"987754\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987754\"]65 centimeters[\/hidden-answer]\r\n\r\nA typical dove weighs [latex]345[\/latex] grams. A typical duck weighs [latex]1.2[\/latex] kilograms. What is the difference, in grams, of the weights of a duck and a dove?\r\n\r\nConcetta had a [latex]\\text{2-kilogram}[\/latex] bag of flour. She used [latex]180[\/latex] grams of flour to make biscotti. How many kilograms of flour are left in the bag?\r\n\r\n[reveal-answer q=\"987854\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987854\"]1.82 kilograms[\/hidden-answer]\r\n\r\nHarry mailed [latex]5[\/latex] packages that weighed [latex]420[\/latex] grams each. What was the total weight of the packages in kilograms?\r\n\r\nOne glass of orange juice provides [latex]560[\/latex] milligrams of potassium. Linda drinks one glass of orange juice every morning. How many grams of potassium does Linda get from her orange juice in [latex]30[\/latex] days?\r\n\r\n[reveal-answer q=\"987954\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987954\"]16.8 grams[\/hidden-answer]\r\n\r\nJonas drinks [latex]200[\/latex] milliliters of water [latex]8[\/latex] times a day. How many liters of water does Jonas drink in a day?\r\n\r\nOne serving of whole grain sandwich bread provides [latex]6[\/latex] grams of protein. How many milligrams of protein are provided by [latex]7[\/latex] servings of whole grain sandwich bread?\r\n\r\n[reveal-answer q=\"987054\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987054\"]42,000 milligrams[\/hidden-answer]\r\n\r\nConvert Between U.S. and Metric Systems<\/strong>\r\nIn the following exercises, make the unit conversions. Round to the nearest tenth.<\/strong>\r\n\r\nBill is [latex]75[\/latex] inches tall. Convert his height to centimeters.\r\n\r\nFrankie is [latex]42[\/latex] inches tall. Convert his height to centimeters.\r\n\r\n[reveal-answer q=\"987614\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987614\"]106.7 centimeters[\/hidden-answer]\r\n\r\nMarcus passed a football [latex]24[\/latex] yards. Convert the pass length to meters.\r\n\r\nConnie bought [latex]9[\/latex] yards of fabric to make drapes. Convert the fabric length to meters.\r\n\r\n[reveal-answer q=\"987624\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987624\"]8.2 meters[\/hidden-answer]\r\n\r\nEach American throws out an average of [latex]1,650[\/latex] pounds of garbage per year. Convert this weight to kilograms.\r\n\r\nAn average American will throw away [latex]90,000[\/latex] pounds of trash over his or her lifetime. Convert this weight to kilograms.\r\n\r\n[reveal-answer q=\"987634\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987634\"]41,500 kilograms[\/hidden-answer]\r\n\r\nA [latex]\\text{5K}[\/latex] run is [latex]5[\/latex] kilometers long. Convert this length to miles.\r\n\r\nKathryn is [latex]1.6[\/latex] meters tall. Convert her height to feet.\r\n\r\n[reveal-answer q=\"987644\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987644\"]5.2 feet[\/hidden-answer]\r\n\r\nDawn\u2019s suitcase weighed [latex]20[\/latex] kilograms. Convert the weight to pounds.\r\n\r\nJackson\u2019s backpack weighs [latex]15[\/latex] kilograms. Convert the weight to pounds.\r\n\r\n[reveal-answer q=\"987664\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987664\"]33 pounds[\/hidden-answer]\r\n\r\nOzzie put [latex]14[\/latex] gallons of gas in his truck. Convert the volume to liters.\r\n\r\nBernard bought [latex]8[\/latex] gallons of paint. Convert the volume to liters.\r\n\r\n[reveal-answer q=\"987674\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987674\"]30.4 liters[\/hidden-answer]\r\n\r\nConvert between Fahrenheit and Celsius<\/strong>\r\nIn the following exercises, convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth.\r\n\r\n[latex]86{^\\circ F}[\/latex]\r\n\r\n[latex]77{^\\circ F}[\/latex]\r\n\r\n[reveal-answer q=\"987684\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987684\"]25\u00b0C[\/hidden-answer]\r\n\r\n[latex]104{^\\circ F}[\/latex]\r\n\r\n[latex]14{^\\circ F}[\/latex]\r\n\r\n[reveal-answer q=\"987694\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987694\"]\u221210\u00b0C[\/hidden-answer]\r\n\r\n[latex]72{^\\circ F}[\/latex]\r\n\r\n[latex]4{^\\circ F}[\/latex]\r\n\r\n[reveal-answer q=\"987604\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987604\"]\u221215.5\u00b0C[\/hidden-answer]\r\n\r\n[latex]0{^\\circ F}[\/latex]\r\n\r\n[latex]120{^\\circ F}[\/latex]\r\n\r\n[reveal-answer q=\"987651\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987651\"]48.9\u00b0C[\/hidden-answer]\r\n\r\nIn the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.<\/strong>\r\n\r\n[latex]5{^\\circ C}[\/latex]\r\n\r\n[latex]25{^\\circ C}[\/latex]\r\n\r\n[reveal-answer q=\"987652\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987652\"]77\u00b0F[\/hidden-answer]\r\n\r\n[latex]-10{^\\circ C}[\/latex]\r\n\r\n[latex]-15{^\\circ C}[\/latex]\r\n\r\n[reveal-answer q=\"987653\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987653\"]5\u00b0F[\/hidden-answer]\r\n\r\n[latex]22{^\\circ C}[\/latex]\r\n\r\n[latex]8{^\\circ C}[\/latex]\r\n\r\n[reveal-answer q=\"987655\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987655\"]46.4\u00b0F[\/hidden-answer]\r\n\r\n[latex]43{^\\circ C}[\/latex]\r\n\r\n[latex]16{^\\circ C}[\/latex]\r\n\r\n[reveal-answer q=\"987656\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987656\"]60.8\u00b0F[\/hidden-answer]\r\n

Everyday Math<\/h2>\r\nNutrition<\/strong> Julian drinks one can of soda every day. Each can of soda contains [latex]40[\/latex] grams of sugar. How many kilograms of sugar does Julian get from soda in [latex]1[\/latex] year?\r\n\r\nReflectors<\/strong> The reflectors in each lane-marking stripe on a highway are spaced [latex]16[\/latex] yards apart. How many reflectors are needed for a one-mile-long stretch of highway?\r\n\r\n[reveal-answer q=\"987657\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987657\"]110 reflectors[\/hidden-answer]\r\n

Writing Exercises<\/h2>\r\nSome people think that [latex]65{^\\circ }[\/latex] to [latex]75{^\\circ }[\/latex] Fahrenheit is the ideal temperature range.\r\n\u24d0 What is your ideal temperature range? Why do you think so?\r\n\u24d1 Convert your ideal temperatures from Fahrenheit to Celsius.\r\n\r\n\u24d0 Did you grow up using the U.S. customary or the metric system of measurement? \u24d1 Describe two examples in your life when you had to convert between systems of measurement. \u24d2 Which system do you think is easier to use? Explain.\r\n

Self Check<\/h2>\r\n\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.\r\n\r\n\".\"\r\n\u24d1 Overall, after looking at the checklist, do you think you are well-prepared for the next chapter? Why or why not?\r\n

Systems of Measurement<\/h2>\r\nIn the following exercises, convert between U.S. units. Round to the nearest tenth.<\/strong>\r\n\r\nA floral arbor is [latex]7[\/latex] feet tall. Convert the height to inches.\r\n\r\nA picture frame is [latex]42[\/latex] inches wide. Convert the width to feet.\r\n\r\n[reveal-answer q=\"987658\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987658\"]3.5 feet[\/hidden-answer]\r\n\r\nKelly is [latex]5[\/latex] feet [latex]4[\/latex] inches tall. Convert her height to inches.\r\n\r\nA playground is [latex]45[\/latex] feet wide. Convert the width to yards.\r\n\r\n[reveal-answer q=\"987659\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987659\"]15 yards[\/hidden-answer]\r\n\r\nThe height of Mount Shasta is [latex]14,179[\/latex] feet. Convert the height to miles.\r\n\r\nShamu weighs [latex]4.5[\/latex] tons. Convert the weight to pounds.\r\n\r\n[reveal-answer q=\"987650\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987650\"]9000 pounds[\/hidden-answer]\r\n\r\nThe play lasted [latex]1\\Large\\frac{3}{4}[\/latex] hours. Convert the time to minutes.\r\n\r\nHow many tablespoons are in a quart?\r\n\r\n[reveal-answer q=\"117654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"117654\"]64 tablespoons[\/hidden-answer]\r\n\r\nNaomi\u2019s baby weighed [latex]5[\/latex] pounds [latex]14[\/latex] ounces at birth. Convert the weight to ounces.\r\n\r\nTrinh needs [latex]30[\/latex] cups of paint for her class art project. Convert the volume to gallons.\r\n\r\n[reveal-answer q=\"227654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"227654\"]1.9 gallons[\/hidden-answer]\r\n\r\nIn the following exercises, solve, and state your answer in mixed units.<\/strong>\r\n\r\nJohn caught [latex]4[\/latex] lobsters. The weights of the lobsters were [latex]1[\/latex] pound [latex]9[\/latex] ounces, [latex]1[\/latex] pound [latex]12[\/latex] ounces, [latex]4[\/latex] pounds [latex]2[\/latex] ounces, and [latex]2[\/latex] pounds [latex]15[\/latex] ounces. What was the total weight of the lobsters?\r\n\r\nEvery day last week, Pedro recorded the amount of time he spent reading. He read for [latex]50,25,83,45,32,60,\\text{and}135[\/latex] minutes. How much time, in hours and minutes, did Pedro spend reading?\r\n\r\n[reveal-answer q=\"337654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"337654\"]7 hours 10 minutes[\/hidden-answer]\r\n\r\nFouad is [latex]6[\/latex] feet [latex]2[\/latex] inches tall. If he stands on a rung of a ladder [latex]8[\/latex] feet [latex]10[\/latex] inches high, how high off the ground is the top of Fouad\u2019s head?\r\n\r\nDalila wants to make pillow covers. Each cover takes [latex]30[\/latex] inches of fabric. How many yards and inches of fabric does she need for [latex]4[\/latex] pillow covers?\r\n\r\n[reveal-answer q=\"447654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"447654\"]3 yards, 12 inches[\/hidden-answer]\r\n\r\nIn the following exercises, convert between metric units.<\/strong>\r\n\r\nDonna is [latex]1.7[\/latex] meters tall. Convert her height to centimeters.\r\n\r\nMount Everest is [latex]8,850[\/latex] meters tall. Convert the height to kilometers.\r\n\r\n[reveal-answer q=\"557654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"557654\"]8.85 kilometers[\/hidden-answer]\r\n\r\nOne cup of yogurt contains [latex]488[\/latex] milligrams of calcium. Convert this to grams.\r\n\r\nOne cup of yogurt contains [latex]13[\/latex] grams of protein. Convert this to milligrams.\r\n\r\n[reveal-answer q=\"667654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"667654\"]13,000 milligrams[\/hidden-answer]\r\n\r\nSergio weighed [latex]2.9[\/latex] kilograms at birth. Convert this to grams.\r\n\r\nA bottle of water contained [latex]650[\/latex] milliliters. Convert this to liters.\r\n\r\n[reveal-answer q=\"777654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"777654\"]0.65 liters[\/hidden-answer]\r\n\r\nIn the following exercises, solve.<\/strong>\r\n\r\nMinh is [latex]2[\/latex] meters tall. His daughter is [latex]88[\/latex] centimeters tall. How much taller, in meters, is Minh than his daughter?\r\n\r\nSelma had a [latex]\\text{1-liter}[\/latex] bottle of water. If she drank [latex]145[\/latex] milliliters, how much water, in milliliters, was left in the bottle?\r\n\r\n[reveal-answer q=\"911654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"911654\"]855 milliliters[\/hidden-answer]\r\n\r\nOne serving of cranberry juice contains [latex]30[\/latex] grams of sugar. How many kilograms of sugar are in [latex]30[\/latex] servings of cranberry juice?\r\n\r\nOne ounce of tofu provides [latex]2[\/latex] grams of protein. How many milligrams of protein are provided by [latex]5[\/latex] ounces of tofu?\r\n\r\n[reveal-answer q=\"922654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"922654\"]10,000 milligrams[\/hidden-answer]\r\n\r\nIn the following exercises, convert between U.S. and metric units. Round to the nearest tenth.<\/strong>\r\n\r\nMajid is [latex]69[\/latex] inches tall. Convert his height to centimeters.\r\n\r\nA college basketball court is [latex]84[\/latex] feet long. Convert this length to meters.\r\n\r\n[reveal-answer q=\"933654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"933654\"]25.6 meters[\/hidden-answer]\r\n\r\nCaroline walked [latex]2.5[\/latex] kilometers. Convert this length to miles.\r\n\r\nLucas weighs [latex]78[\/latex] kilograms. Convert his weight to pounds.\r\n\r\n[reveal-answer q=\"944654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"944654\"]171.6 pounds[\/hidden-answer]\r\n\r\nSteve\u2019s car holds [latex]55[\/latex] liters of gas. Convert this to gallons.\r\n\r\nA box of books weighs [latex]25[\/latex] pounds. Convert this weight to kilograms.\r\n\r\n[reveal-answer q=\"955654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"955654\"]11.4 kilograms[\/hidden-answer]\r\n\r\nIn the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.<\/strong>\r\n\r\n[latex]95{^\\circ F}[\/latex]\r\n\r\n[latex]23{^\\circ F}[\/latex]\r\n\r\n[reveal-answer q=\"966654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"966654\"]\u22125\u00b0C[\/hidden-answer]\r\n\r\n[latex]20{^\\circ F}[\/latex]\r\n\r\n[latex]64{^\\circ F}[\/latex]\r\n\r\n[reveal-answer q=\"999654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"999654\"]17.8\u00b0C[\/hidden-answer]\r\n\r\nIn the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.<\/strong>\r\n\r\n[latex]30{^\\circ C}[\/latex]\r\n\r\n[latex]-5{^\\circ C}[\/latex]\r\n\r\n[reveal-answer q=\"981154\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"981154\"]23\u00b0F[\/hidden-answer]\r\n\r\n[latex]-12{^\\circ C}[\/latex]\r\n\r\n[latex]24{^\\circ C}[\/latex]\r\n\r\n[reveal-answer q=\"982254\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"982254\"]75.2\u00b0F[\/hidden-answer]\r\n\r\nIn the following exercises, solve using the appropriate unit conversions.<\/strong>\r\n\r\nAzize walked [latex]4\\Large\\frac{1}{2}[\/latex] miles. Convert this distance to feet. [latex]\\text{(1 mile}=\\text{5,280 feet).}[\/latex]\r\n\r\nOne cup of milk contains [latex]276[\/latex] milligrams of calcium. Convert this to grams. [latex]\\text{(1 milligram}=\\text{0.001 gram)}[\/latex]\r\n\r\n[reveal-answer q=\"000654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"000654\"].276 grams[\/hidden-answer]\r\n\r\nLarry had [latex]5[\/latex] phone customer phone calls yesterday. The calls lasted [latex]28,44,9,75,\\text{and}55[\/latex] minutes. How much time, in hours and minutes, did Larry spend on the phone? [latex]\\text{(1 hour}=\\text{60 minutes)}[\/latex]\r\n\r\nJanice ran [latex]15[\/latex] kilometers. Convert this distance to miles. Round to the nearest hundredth of a mile. [latex]\\text{(1 mile}=\\text{1.61 kilometers)}[\/latex]\r\n\r\n[reveal-answer q=\"111654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"111654\"]9.317 miles[\/hidden-answer]\r\n\r\nYolie is [latex]63[\/latex] inches tall. Convert her height to centimeters. Round to the nearest centimeter. [latex]\\text{(1 inch}=\\text{2.54 centimeters)}[\/latex]\r\n\r\nUse the formula [latex]F=\\Large\\frac{9}{5}\\normalsize C+32[\/latex] to convert [latex]35{^\\circ C}[\/latex] to degrees [latex]\\text{F}[\/latex]\r\n\r\n[reveal-answer q=\"222654\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"222654\"]95\u00b0F<\/em>[\/hidden-answer]\r\n\r\n \r\n

Contribute!<\/h2>
Did you have an idea for improving this content? We\u2019d love your input.<\/div>Improve this page<\/a>Learn More<\/a>","rendered":"

Practice Makes Perfect<\/h2>\n

Use the Properties of Angles<\/strong>
\nIn the following exercises, find \u24d0 the supplement and \u24d1 the complement of the given angle.<\/strong><\/p>\n

[latex]{53^\\circ }[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 127\u00b0
\n\u24d1 37\u00b0<\/p>\n<\/div>\n<\/div>\n

[latex]{16^\\circ }[\/latex]<\/p>\n

[latex]{29^\\circ }[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 151\u00b0
\n\u24d1 61\u00b0<\/p>\n<\/div>\n<\/div>\n

[latex]{72^\\circ }[\/latex]<\/p>\n

In the following exercises, use the properties of angles to solve.<\/strong><\/p>\n

Find the supplement of a [latex]{135^\\circ }[\/latex] angle.<\/p>\n

Show Solution<\/span><\/p>\n
\n

45\u00b0<\/p>\n<\/div>\n<\/div>\n

Find the complement of a [latex]{38^\\circ }[\/latex] angle.<\/p>\n

Find the complement of a [latex]27.5^\\circ[\/latex] angle.<\/p>\n

Show Solution<\/span><\/p>\n
\n

62.5\u00b0<\/p>\n<\/div>\n<\/div>\n

Find the supplement of a [latex]109.5^\\circ[\/latex] angle.<\/p>\n

Two angles are supplementary. The larger angle is [latex]{56^\\circ }[\/latex] more than the smaller angle. Find the measures of both angles.<\/p>\n

Show Solution<\/span><\/p>\n
\n

62\u00b0, 118\u00b0<\/p>\n<\/div>\n<\/div>\n

Two angles are supplementary. The smaller angle is [latex]{36^\\circ }[\/latex] less than the larger angle. Find the measures of both angles.<\/p>\n

Two angles are complementary. The smaller angle is [latex]{34^\\circ }[\/latex] less than the larger angle. Find the measures of both angles.<\/p>\n

Show Solution<\/span><\/p>\n
\n

62\u00b0, 28\u00b0<\/p>\n<\/div>\n<\/div>\n

Two angles are complementary. The larger angle is [latex]{52^\\circ }[\/latex] more than the smaller angle. Find the measures of both angles.<\/p>\n

Use the Properties of Triangles<\/strong><\/p>\n

In the following exercises, solve using properties of triangles<\/strong>.<\/p>\n

The measures of two angles of a triangle are [latex]{26^\\circ }[\/latex] and [latex]{98^\\circ }[\/latex]. Find the measure of the third angle.<\/p>\n

Show Solution<\/span><\/p>\n
\n

56\u00b0<\/p>\n<\/div>\n<\/div>\n

The measures of two angles of a triangle are [latex]{61^\\circ }[\/latex] and [latex]{84^\\circ }[\/latex]. Find the measure of the third angle.<\/p>\n

The measures of two angles of a triangle are [latex]{105^\\circ }[\/latex] and [latex]{31^\\circ }[\/latex]. Find the measure of the third angle.<\/p>\n

Show Solution<\/span><\/p>\n
\n

44\u00b0<\/p>\n<\/div>\n<\/div>\n

The measures of two angles of a triangle are [latex]{47^\\circ }[\/latex] and [latex]{72^\\circ }[\/latex]. Find the measure of the third angle.<\/p>\n

One angle of a right triangle measures [latex]{33^\\circ }[\/latex]. What is the measure of the other angle?<\/p>\n

Show Solution<\/span><\/p>\n
\n

57\u00b0<\/p>\n<\/div>\n<\/div>\n

One angle of a right triangle measures [latex]{51^\\circ }[\/latex]. What is the measure of the other angle?<\/p>\n

One angle of a right triangle measures [latex]22.5^\\circ[\/latex]. What is the measure of the other angle?<\/p>\n

Show Solution<\/span><\/p>\n
\n

67.5\u00b0<\/p>\n<\/div>\n<\/div>\n

One angle of a right triangle measures [latex]36.5^\\circ[\/latex]. What is the measure of the other angle?<\/p>\n

The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.<\/p>\n

Show Solution<\/span><\/p>\n
\n

45\u00b0, 45\u00b0, 90\u00b0<\/p>\n<\/div>\n<\/div>\n

The measure of the smallest angle of a right triangle is [latex]{20^\\circ }[\/latex] less than the measure of the other small angle. Find the measures of all three angles.<\/p>\n

The angles in a triangle are such that the measure of one angle is twice the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.<\/p>\n

Show Solution<\/span><\/p>\n
\n

30\u00b0, 60\u00b0, 90\u00b0<\/p>\n<\/div>\n<\/div>\n

The angles in a triangle are such that the measure of one angle is [latex]{20^\\circ }[\/latex] more than the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.<\/p>\n

Find the Length of the Missing Side<\/strong><\/p>\n

In the following exercises, [latex]\\Delta ABC[\/latex] is similar to [latex]\\Delta XYZ[\/latex]. Find the length of the indicated side.<\/strong><\/p>\n

\"Two<\/p>\n

side [latex]b[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
\n

12<\/p>\n<\/div>\n<\/div>\n

side [latex]x[\/latex]<\/p>\n

On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides are shown in the figure below. The actual distance from Los Angeles to Las Vegas is [latex]270[\/latex] miles.<\/p>\n

\"A<\/p>\n

Find the distance from Los Angeles to San Francisco.<\/p>\n

Show Solution<\/span><\/p>\n
\n

351 miles<\/p>\n<\/div>\n<\/div>\n

Find the distance from San Francisco to Las Vegas.<\/p>\n

Use the Pythagorean Theorem<\/strong><\/p>\n

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse<\/strong>.<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

15<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

25<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

Find the Length of the Missing Side<\/strong><\/p>\n

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.<\/strong><\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

8<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

12<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

10.2<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

8<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

In the following exercises, solve. Approximate to the nearest tenth, if necessary.<\/strong><\/p>\n

A [latex]\\text{13-foot}[\/latex] string of lights will be attached to the top of a [latex]\\text{12-foot}[\/latex] pole for a holiday display. How far from the base of the pole should the end of the string of lights be anchored?<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

5 feet<\/p>\n<\/div>\n<\/div>\n

Pam wants to put a banner across her garage door to congratulate her son on his college graduation. The garage door is [latex]12[\/latex] feet high and [latex]16[\/latex] feet wide. How long should the banner be to fit the garage door?<\/p>\n

\"A<\/p>\n

Chi is planning to put a path of paving stones through her flower garden. The flower garden is a square with sides of [latex]10[\/latex] feet. What will the length of the path be?<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

14.1 feet<\/p>\n<\/div>\n<\/div>\n

Brian borrowed a [latex]\\text{20-foot}[\/latex] extension ladder to paint his house. If he sets the base of the ladder [latex]6[\/latex] feet from the house, how far up will the top of the ladder reach?<\/p>\n

\"A<\/p>\n

Everyday Math<\/h2>\n

Building a scale model<\/strong> Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is [latex]30[\/latex] feet wide and [latex]35[\/latex] feet tall at the highest point of the roof. If the dollhouse will be [latex]2.5[\/latex] feet wide, how tall will its highest point be?<\/p>\n

Show Solution<\/span><\/p>\n
\n

2.9 feet<\/p>\n<\/div>\n<\/div>\n

Measurement<\/strong> A city engineer plans to build a footbridge across a lake from point [latex]\\text{X}[\/latex] to point [latex]\\text{Y}[\/latex], as shown in the picture below. To find the length of the footbridge, she draws a right triangle [latex]\\text{XYZ}[\/latex], with right angle at [latex]\\text{X}[\/latex]. She measures the distance from [latex]\\text{X}[\/latex] to [latex]\\text{Z},800[\/latex] feet, and from [latex]\\text{Y}[\/latex] to [latex]\\text{Z},1,000[\/latex] feet. How long will the bridge be?<\/p>\n

\"A<\/p>\n

Writing Exercises<\/h2>\n

Write three of the properties of triangles from this section and then explain each in your own words.<\/p>\n

Answers will vary.<\/p>\n

Explain how the figure below illustrates the Pythagorean Theorem for a triangle with legs of length [latex]3[\/latex] and [latex]4[\/latex].<\/p>\n

\"Three<\/p>\n

Self Check<\/h2>\n

\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

\".\"
\n\u24d1 What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p>\n

<\/h2>\n

Use Properties of Angles, Triangles, and the Pythagorean Theorem<\/h2>\n

Use Properties of Angles<\/strong>
\nIn the following exercises, solve using properties of angles.<\/p>\n

What is the supplement of a [latex]{48^\\circ }[\/latex] angle?<\/p>\n

Show Solution<\/span><\/p>\n
\n

132\u00b0<\/p>\n<\/div>\n<\/div>\n

What is the complement of a [latex]{61^\\circ }[\/latex] angle?<\/p>\n

Two angles are complementary. The smaller angle is [latex]{24^\\circ }[\/latex] less than the larger angle. Find the measures of both angles.<\/p>\n

Show Solution<\/span><\/p>\n
\n

33\u00b0, 57\u00b0<\/p>\n<\/div>\n<\/div>\n

Two angles are supplementary. The larger angle is [latex]{45^\\circ }[\/latex] more than the smaller angle. Find the measures of both angles.<\/p>\n

Use Properties of Triangles<\/strong>
\nIn the following exercises, solve using properties of triangles.<\/strong><\/p>\n

The measures of two angles of a triangle are [latex]22[\/latex] and [latex]85[\/latex] degrees. Find the measure of the third angle.<\/p>\n

Show Solution<\/span><\/p>\n
\n

73\u00b0<\/p>\n<\/div>\n<\/div>\n

One angle of a right triangle measures [latex]41.5[\/latex] degrees. What is the measure of the other small angle?<\/p>\n

One angle of a triangle is [latex]{30^\\circ }[\/latex] more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.<\/p>\n

Show Solution<\/span><\/p>\n
\n

30\u00b0, 60\u00b0, 90\u00b0<\/p>\n<\/div>\n<\/div>\n

One angle of a triangle is twice the measure of the smallest angle. The third angle is [latex]{60^\\circ }[\/latex] more than the measure of the smallest angle. Find the measures of all three angles.<\/p>\n

In the following exercises, [latex]\\Delta ABC[\/latex] is similar to [latex]\\Delta XYZ[\/latex]. Find the length of the indicated side.<\/strong><\/p>\n

\"Two<\/p>\n

side [latex]x[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
\n

15<\/p>\n<\/div>\n<\/div>\n

side [latex]b[\/latex]<\/p>\n

Use the Pythagorean Theorem<\/strong>
\nIn the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.<\/strong><\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

26<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

8<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

8.1<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

In the following exercises, solve. Approximate to the nearest tenth, if necessary.<\/strong><\/p>\n

Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is [latex]8[\/latex] feet tall and Sergio has [latex]10[\/latex] feet of wire. How far from the base of the antenna can he attach the wire?<\/p>\n

\"An<\/p>\n

Show Solution<\/span><\/p>\n
\n

6 feet<\/p>\n<\/div>\n<\/div>\n

Seong is building shelving in his garage. The shelves are [latex]36[\/latex] inches wide and [latex]15[\/latex] inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?<\/p>\n

\"A<\/p>\n

Use Properties of Rectangles, Triangles, and Trapezoids<\/h2>\n

Understand Linear, Square, Cubic Measure<\/strong>
\nIn the following exercises, would you measure each item using linear, square, or cubic measure?<\/strong><\/p>\n

amount of sand in a sandbag<\/p>\n

Show Solution<\/span><\/p>\n
\n

cubic<\/p>\n<\/div>\n<\/div>\n

height of a tree<\/p>\n

size of a patio<\/p>\n

Show Solution<\/span><\/p>\n
\n

square<\/p>\n<\/div>\n<\/div>\n

length of a highway<\/p>\n

In the following exercises, find<\/strong><\/p>\n

\u24d0 the perimeter<\/strong>
\n\u24d1 the area of each figure<\/strong><\/p>\n

\"Three<\/p>\n

\u24d0 8 units
\n\u24d1 3 sq. units<\/p>\n

\"Five<\/p>\n

Use Properties of Rectangles<\/strong><\/p>\n

In the following exercises, find the<\/strong><\/p>\n

\u24d0 perimeter<\/strong>
\n\u24d1 area of each rectangle<\/strong><\/p>\n

The length of a rectangle is [latex]42[\/latex] meters and the width is [latex]28[\/latex] meters.<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 140 m
\n\u24d1 1176 sq. m<\/p>\n<\/div>\n<\/div>\n

The length of a rectangle is [latex]36[\/latex] feet and the width is [latex]19[\/latex] feet.<\/p>\n

A sidewalk in front of Kathy\u2019s house is in the shape of a rectangle [latex]4[\/latex] feet wide by [latex]45[\/latex] feet long.<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 98 ft.
\n\u24d1 180 sq. ft.<\/p>\n<\/div>\n<\/div>\n

A rectangular room is [latex]16[\/latex] feet wide by [latex]12[\/latex] feet long.<\/p>\n

In the following exercises, solve.<\/strong><\/p>\n

Find the length of a rectangle with perimeter of [latex]220[\/latex] centimeters and width of [latex]85[\/latex] centimeters.<\/p>\n

Show Solution<\/span><\/p>\n
\n

25 cm<\/p>\n<\/div>\n<\/div>\n

Find the width of a rectangle with perimeter [latex]39[\/latex] and length [latex]11[\/latex].<\/p>\n

The area of a rectangle is [latex]2356[\/latex] square meters. The length is [latex]38[\/latex] meters. What is the width?<\/p>\n

Show Solution<\/span><\/p>\n
\n

62 m<\/p>\n<\/div>\n<\/div>\n

The width of a rectangle is [latex]45[\/latex] centimeters. The area is [latex]2700[\/latex] square centimeters. What is the length?<\/p>\n

The length of a rectangle is [latex]12[\/latex] centimeters more than the width. The perimeter is [latex]74[\/latex] centimeters. Find the length and the width.<\/p>\n

Show Solution<\/span><\/p>\n
\n

24.5 in., 12.5 in.<\/p>\n<\/div>\n<\/div>\n

The width of a rectangle is [latex]3[\/latex] more than twice the length. The perimeter is [latex]96[\/latex] inches. Find the length and the width.<\/p>\n

Use Properties of Triangles<\/strong>
\nIn the following exercises, solve using the properties of triangles.<\/p>\n

Find the area of a triangle with base [latex]18[\/latex] inches and height [latex]15[\/latex] inches.<\/p>\n

Show Solution<\/span><\/p>\n
\n

135 sq. in.<\/p>\n<\/div>\n<\/div>\n

Find the area of a triangle with base [latex]33[\/latex] centimeters and height [latex]21[\/latex] centimeters.<\/p>\n

A triangular road sign has base [latex]30[\/latex] inches and height [latex]40[\/latex] inches. What is its area?<\/p>\n

Show Solution<\/span><\/p>\n
\n

600 sq. in.<\/p>\n<\/div>\n<\/div>\n

If a triangular courtyard has sides [latex]9[\/latex] feet and [latex]12[\/latex] feet and the perimeter is [latex]32[\/latex] feet, how long is the third side?<\/p>\n

A tile in the shape of an isosceles triangle has a base of [latex]6[\/latex] inches. If the perimeter is [latex]20[\/latex] inches, find the length of each of the other sides.<\/p>\n

Show Solution<\/span><\/p>\n
\n

7 in., 7 in.<\/p>\n<\/div>\n<\/div>\n

Find the length of each side of an equilateral triangle with perimeter of [latex]81[\/latex] yards.<\/p>\n

The perimeter of a triangle is [latex]59[\/latex] feet. One side of the triangle is [latex]3[\/latex] feet longer than the shortest side. The third side is [latex]5[\/latex] feet longer than the shortest side. Find the length of each side.<\/p>\n

Show Solution<\/span><\/p>\n
\n

17 ft., 20 ft., 22 ft.<\/p>\n<\/div>\n<\/div>\n

One side of a triangle is three times the smallest side. The third side is [latex]9[\/latex] feet more than the shortest side. The perimeter is [latex]39[\/latex] feet. Find the lengths of all three sides.<\/p>\n

Use Properties of Trapezoids<\/strong>
\nIn the following exercises, solve using the properties of trapezoids.<\/strong><\/p>\n

The height of a trapezoid is [latex]8[\/latex] feet and the bases are [latex]11[\/latex] and [latex]14[\/latex] feet. What is the area?<\/p>\n

Show Solution<\/span><\/p>\n
\n

100 sq. ft.<\/p>\n<\/div>\n<\/div>\n

The height of a trapezoid is [latex]5[\/latex] yards and the bases are [latex]7[\/latex] and [latex]10[\/latex] yards. What is the area?<\/p>\n

Find the area of the trapezoid with height [latex]25[\/latex] meters and bases [latex]32.5[\/latex] and [latex]21.5[\/latex] meters.<\/p>\n

Show Solution<\/span><\/p>\n
\n

675 sq. m<\/p>\n<\/div>\n<\/div>\n

A flag is shaped like a trapezoid with height [latex]62[\/latex] centimeters and the bases are [latex]91.5[\/latex] and [latex]78.1[\/latex] centimeters. What is the area of the flag?<\/p>\n

Practice Makes Perfect<\/h2>\n

Understand Linear, Square, and Cubic Measure<\/strong>
\nIn the following exercises, determine whether you would measure each item using linear, square, or cubic units.<\/strong><\/p>\n

amount of water in a fish tank<\/p>\n

Show Solution<\/span><\/p>\n
\n

cubic<\/p>\n<\/div>\n<\/div>\n

length of dental floss<\/p>\n

living area of an apartment<\/p>\n

Show Solution<\/span><\/p>\n
\n

square<\/p>\n<\/div>\n<\/div>\n

floor space of a bathroom tile<\/p>\n

height of a doorway<\/p>\n

Show Solution<\/span><\/p>\n
\n

linear<\/p>\n<\/div>\n<\/div>\n

capacity of a truck trailer<\/p>\n

In the following exercises, find the \u24d0 perimeter and \u24d1 area of each figure. Assume each side of the square is [latex]1[\/latex] cm.<\/strong><\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 10 cm
\n\u24d1 4 sq. cm<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

\"Three<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 8 cm
\n\u24d1 3 sq. cm<\/p>\n<\/div>\n<\/div>\n

\"Four<\/p>\n

\"Five<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 10 cm
\n\u24d1 5 sq. cm<\/p>\n<\/div>\n<\/div>\n

\"A<\/p>\n

Use the Properties of Rectangles<\/strong>
\nIn the following exercises, find the \u24d0 perimeter and \u24d1 area of each rectangle.<\/strong><\/p>\n

The length of a rectangle is [latex]85[\/latex] feet and the width is [latex]45[\/latex] feet.<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 260 ft
\n\u24d1 3825 sq. ft<\/p>\n<\/div>\n<\/div>\n

The length of a rectangle is [latex]26[\/latex] inches and the width is [latex]58[\/latex] inches.<\/p>\n

A rectangular room is [latex]15[\/latex] feet wide by [latex]14[\/latex] feet long.<\/p>\n

Show Solution<\/span><\/p>\n
\n

\u24d0 58 ft
\n\u24d1 210 sq. ft<\/p>\n<\/div>\n<\/div>\n

A driveway is in the shape of a rectangle [latex]20[\/latex] feet wide by [latex]35[\/latex] feet long.<\/p>\n

In the following exercises, solve.<\/strong><\/p>\n

Find the length of a rectangle with perimeter [latex]124[\/latex] inches and width [latex]38[\/latex] inches.<\/p>\n

Show Solution<\/span><\/p>\n
\n

24 inches<\/p>\n<\/div>\n<\/div>\n

Find the length of a rectangle with perimeter [latex]20.2[\/latex] yards and width of [latex]7.8[\/latex] yards.<\/p>\n

Find the width of a rectangle with perimeter [latex]92[\/latex] meters and length [latex]19[\/latex] meters.<\/p>\n

Show Solution<\/span><\/p>\n
\n

27 meters<\/p>\n<\/div>\n<\/div>\n

Find the width of a rectangle with perimeter [latex]16.2[\/latex] meters and length [latex]3.2[\/latex] meters.<\/p>\n

The area of a rectangle is [latex]414[\/latex] square meters. The length is [latex]18[\/latex] meters. What is the width?<\/p>\n

Show Solution<\/span><\/p>\n
\n

23 m<\/p><\/div>\n<\/div>\n

The area of a rectangle is [latex]782[\/latex] square centimeters. The width is [latex]17[\/latex] centimeters. What is the length?<\/p>\n

The length of a rectangle is [latex]9[\/latex] inches more than the width. The perimeter is [latex]46[\/latex] inches. Find the length and the width.<\/p>\n

Show Solution<\/span><\/p>\n
7 in., 16 in.<\/div>\n<\/div>\n

The width of a rectangle is [latex]8[\/latex] inches more than the length. The perimeter is [latex]52[\/latex] inches. Find the length and the width.<\/p>\n

The perimeter of a rectangle is [latex]58[\/latex] meters. The width of the rectangle is [latex]5[\/latex] meters less than the length. Find the length and the width of the rectangle.<\/p>\n

Show Solution<\/span><\/p>\n
17 m, 12 m<\/div>\n<\/div>\n

The perimeter of a rectangle is [latex]62[\/latex] feet. The width is [latex]7[\/latex] feet less than the length. Find the length and the width.<\/p>\n

The width of the rectangle is [latex]0.7[\/latex] meters less than the length. The perimeter of a rectangle is [latex]52.6[\/latex] meters. Find the dimensions of the rectangle.<\/p>\n

Show Solution<\/span><\/p>\n
13.5 m, 12.8 m<\/div>\n<\/div>\n

The length of the rectangle is [latex]1.1[\/latex] meters less than the width. The perimeter of a rectangle is [latex]49.4[\/latex] meters. Find the dimensions of the rectangle.<\/p>\n

The perimeter of a rectangle of [latex]150[\/latex] feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.<\/p>\n

Show Solution<\/span><\/p>\n
25 ft, 50 ft<\/div>\n<\/div>\n

The length of a rectangle is three times the width. The perimeter is [latex]72[\/latex] feet. Find the length and width of the rectangle.<\/span><\/p>\n

The length of a rectangle is [latex]3[\/latex] meters less than twice the width. The perimeter is [latex]36[\/latex] meters. Find the length and width.<\/p>\n

Show Solution<\/span><\/p>\n
7 m, 11 m<\/div>\n<\/div>\n

The length of a rectangle is [latex]5[\/latex] inches more than twice the width. The perimeter is [latex]34[\/latex] inches. Find the length and width.<\/p>\n

The width of a rectangular window is [latex]24[\/latex] inches. The area is [latex]624[\/latex] square inches. What is the length?<\/p>\n

Show Solution<\/span><\/p>\n
26 in.<\/div>\n<\/div>\n

The length of a rectangular poster is [latex]28[\/latex] inches. The area is [latex]1316[\/latex] square inches. What is the width?<\/p>\n

The area of a rectangular roof is [latex]2310[\/latex] square meters. The length is [latex]42[\/latex] meters. What is the width?<\/p>\n

Show Solution<\/span><\/p>\n
55 m<\/div>\n<\/div>\n

The area of a rectangular tarp is [latex]132[\/latex] square feet. The width is [latex]12[\/latex] feet. What is the length?<\/p>\n

The perimeter of a rectangular courtyard is [latex]160[\/latex] feet. The length is [latex]10[\/latex] feet more than the width. Find the length and the width.<\/p>\n

Show Solution<\/span><\/p>\n
35 ft, 45 ft<\/div>\n<\/div>\n

The perimeter of a rectangular painting is [latex]306[\/latex] centimeters. The length is [latex]17[\/latex] centimeters more than the width. Find the length and the width.<\/p>\n

The width of a rectangular window is [latex]40[\/latex] inches less than the height. The perimeter of the doorway is [latex]224[\/latex] inches. Find the length and the width.<\/p>\n

Show Solution<\/span><\/p>\n
76 in., 36 in.<\/div>\n<\/div>\n

The width of a rectangular playground is [latex]7[\/latex] meters less than the length. The perimeter of the playground is [latex]46[\/latex] meters. Find the length and the width.<\/p>\n

Use the Properties of Triangles<\/strong>
\nIn the following exercises, solve using the properties of triangles.<\/strong><\/p>\n

Find the area of a triangle with base [latex]12[\/latex] inches and height [latex]5[\/latex] inches.<\/p>\n

Show Solution<\/span><\/p>\n
60 sq. in.<\/div>\n<\/div>\n

Find the area of a triangle with base [latex]45[\/latex] centimeters and height [latex]30[\/latex] centimeters.<\/p>\n

Find the area of a triangle with base [latex]8.3[\/latex] meters and height [latex]6.1[\/latex] meters.<\/p>\n

Show Solution<\/span><\/p>\n
25.315 sq. m<\/div>\n<\/div>\n

Find the area of a triangle with base [latex]24.2[\/latex] feet and height [latex]20.5[\/latex] feet.<\/p>\n

A triangular flag has base of [latex]1[\/latex] foot and height of [latex]1.5[\/latex] feet. What is its area?<\/p>\n

Show Solution<\/span><\/p>\n
0.75 sq. ft<\/div>\n<\/div>\n

A triangular window has base of [latex]8[\/latex] feet and height of [latex]6[\/latex] feet. What is its area?<\/p>\n

If a triangle has sides of [latex]6[\/latex] feet and [latex]9[\/latex] feet and the perimeter is [latex]23[\/latex] feet, how long is the third side?<\/p>\n

Show Solution<\/span><\/p>\n
8 ft<\/div>\n<\/div>\n

If a triangle has sides of [latex]14[\/latex] centimeters and [latex]18[\/latex] centimeters and the perimeter is [latex]49[\/latex] centimeters, how long is the third side?<\/p>\n

What is the base of a triangle with an area of [latex]207[\/latex] square inches and height of [latex]18[\/latex] inches?<\/p>\n

Show Solution<\/span><\/p>\n
23 in.<\/div>\n<\/div>\n

What is the height of a triangle with an area of [latex]893[\/latex] square inches and base of [latex]38[\/latex] inches?<\/p>\n

The perimeter of a triangular reflecting pool is [latex]36[\/latex] yards. The lengths of two sides are [latex]10[\/latex] yards and [latex]15[\/latex] yards. How long is the third side?<\/p>\n

Show Solution<\/span><\/p>\n
11 ft<\/div>\n<\/div>\n

A triangular courtyard has perimeter of [latex]120[\/latex] meters. The lengths of two sides are [latex]30[\/latex] meters and [latex]50[\/latex] meters. How long is the third side?<\/p>\n

An isosceles triangle has a base of [latex]20[\/latex] centimeters. If the perimeter is [latex]76[\/latex] centimeters, find the length of each of the other sides.<\/p>\n

Show Solution<\/span><\/p>\n
28 cm<\/div>\n<\/div>\n

An isosceles triangle has a base of [latex]25[\/latex] inches. If the perimeter is [latex]95[\/latex] inches, find the length of each of the other sides.<\/p>\n

Find the length of each side of an equilateral triangle with a perimeter of [latex]51[\/latex] yards.<\/p>\n

Show Solution<\/span><\/p>\n
17 ft<\/div>\n<\/div>\n

Find the length of each side of an equilateral triangle with a perimeter of [latex]54[\/latex] meters.<\/p>\n

The perimeter of an equilateral triangle is [latex]18[\/latex] meters. Find the length of each side.<\/p>\n

Show Solution<\/span><\/p>\n
6 m<\/div>\n<\/div>\n

The perimeter of an equilateral triangle is [latex]42[\/latex] miles. Find the length of each side.<\/p>\n

The perimeter of an isosceles triangle is [latex]42[\/latex] feet. The length of the shortest side is [latex]12[\/latex] feet. Find the length of the other two sides.<\/p>\n

Show Solution<\/span><\/p>\n
15 ft<\/div>\n<\/div>\n

The perimeter of an isosceles triangle is [latex]83[\/latex] inches. The length of the shortest side is [latex]24[\/latex] inches. Find the length of the other two sides.<\/span><\/p>\n

A dish is in the shape of an equilateral triangle. Each side is [latex]8[\/latex] inches long. Find the perimeter.<\/p>\n

Show Solution<\/span><\/p>\n
24 in.<\/div>\n<\/div>\n

A floor tile is in the shape of an equilateral triangle. Each side is [latex]1.5[\/latex] feet long. Find the perimeter.<\/p>\n

A road sign in the shape of an isosceles triangle has a base of [latex]36[\/latex] inches. If the perimeter is [latex]91[\/latex] inches, find the length of each of the other sides.<\/p>\n

Show Solution<\/span><\/p>\n
27.5 in.<\/div>\n<\/div>\n

A scarf in the shape of an isosceles triangle has a base of [latex]0.75[\/latex] meters. If the perimeter is [latex]2[\/latex] meters, find the length of each of the other sides.<\/p>\n

The perimeter of a triangle is [latex]39[\/latex] feet. One side of the triangle is [latex]1[\/latex] foot longer than the second side. The third side is [latex]2[\/latex] feet longer than the second side. Find the length of each side.<\/p>\n

Show Solution<\/span><\/p>\n
12 ft, 13 ft, 14 ft<\/div>\n<\/div>\n

The perimeter of a triangle is [latex]35[\/latex] feet. One side of the triangle is [latex]5[\/latex] feet longer than the second side. The third side is [latex]3[\/latex] feet longer than the second side. Find the length of each side.<\/p>\n

One side of a triangle is twice the smallest side. The third side is [latex]5[\/latex] feet more than the shortest side. The perimeter is [latex]17[\/latex] feet. Find the lengths of all three sides.<\/p>\n

Show Solution<\/span><\/p>\n
3 ft, 6 ft, 8 ft<\/div>\n<\/div>\n

One side of a triangle is three times the smallest side. The third side is [latex]3[\/latex] feet more than the shortest side. The perimeter is [latex]13[\/latex] feet. Find the lengths of all three sides.<\/p>\n

Use the Properties of Trapezoids<\/strong>
\nIn the following exercises, solve using the properties of trapezoids.<\/strong><\/p>\n

The height of a trapezoid is [latex]12[\/latex] feet and the bases are [latex]9[\/latex] and [latex]15[\/latex] feet. What is the area?<\/p>\n

Show Solution<\/span><\/p>\n
144 sq. ft<\/div>\n<\/div>\n

The height of a trapezoid is [latex]24[\/latex] yards and the bases are [latex]18[\/latex] and [latex]30[\/latex] yards. What is the area?<\/p>\n

Find the area of a trapezoid with a height of [latex]51[\/latex] meters and bases of [latex]43[\/latex] and [latex]67[\/latex] meters.<\/p>\n

Show Solution<\/span><\/p>\n
2805 sq. m<\/div>\n<\/div>\n

Find the area of a trapezoid with a height of [latex]62[\/latex] inches and bases of [latex]58[\/latex] and [latex]75[\/latex] inches.<\/p>\n

The height of a trapezoid is [latex]15[\/latex] centimeters and the bases are [latex]12.5[\/latex] and [latex]18.3[\/latex] centimeters. What is the area?<\/p>\n

Show Solution<\/span><\/p>\n
231 sq. cm<\/div>\n<\/div>\n

The height of a trapezoid is [latex]48[\/latex] feet and the bases are [latex]38.6[\/latex] and [latex]60.2[\/latex] feet. What is the area?<\/p>\n

Find the area of a trapezoid with a height of [latex]4.2[\/latex] meters and bases of [latex]8.1[\/latex] and [latex]5.5[\/latex] meters.<\/p>\n

Show Solution<\/span><\/p>\n
28.56 sq. m<\/div>\n<\/div>\n

Find the area of a trapezoid with a height of [latex]32.5[\/latex] centimeters and bases of [latex]54.6[\/latex] and [latex]41.4[\/latex] centimeters.<\/p>\n

Laurel is making a banner shaped like a trapezoid. The height of the banner is [latex]3[\/latex] feet and the bases are [latex]4[\/latex] and [latex]5[\/latex] feet. What is the area of the banner?<\/p>\n

Show Solution<\/span><\/p>\n
13.5 sq. ft<\/div>\n<\/div>\n

Niko wants to tile the floor of his bathroom. The floor is shaped like a trapezoid with width [latex]5[\/latex] feet and lengths [latex]5[\/latex] feet and [latex]8[\/latex] feet. What is the area of the floor?<\/p>\n

Theresa needs a new top for her kitchen counter. The counter is shaped like a trapezoid with width [latex]18.5[\/latex] inches and lengths [latex]62[\/latex] and [latex]50[\/latex] inches. What is the area of the counter?<\/p>\n

Show Solution<\/span><\/p>\n
1036 sq. in.<\/div>\n<\/div>\n

Elena is knitting a scarf. The scarf will be shaped like a trapezoid with width [latex]8[\/latex] inches and lengths [latex]48.2[\/latex] inches and [latex]56.2[\/latex] inches. What is the area of the scarf?<\/span><\/p>\n

Everyday Math<\/h2>\n

Fence<\/strong> Jose just removed the children\u2019s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a [latex]50[\/latex] foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be [latex]10[\/latex] feet. How long can he make the other side if he wants to use the entire roll of fence?<\/p>\n

Show Solution<\/span><\/p>\n
15 ft<\/div>\n<\/div>\n

Gardening<\/strong> Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take [latex]48[\/latex] feet of fencing to enclose the garden. Find the length and width of her garden.<\/p>\n

Fence<\/strong> Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are [latex]6[\/latex] feet, [latex]8[\/latex] feet, and [latex]10[\/latex] feet. The fence costs [latex]$10[\/latex] per foot. How much will it cost for Christa to fence in her flowerbed?<\/p>\n

Show Solution<\/span><\/p>\n
$24<\/div>\n<\/div>\n

Painting<\/strong> Caleb wants to paint one wall of his attic. The wall is shaped like a trapezoid with height [latex]8[\/latex] feet and bases [latex]20[\/latex] feet and [latex]12[\/latex] feet. The cost of the painting one square foot of wall is about [latex]$0.05[\/latex]. About how much will it cost for Caleb to paint the attic wall?<\/p>\n

\"A<\/p>\n

Writing Exercises<\/h2>\n

If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.<\/p>\n

Answers will vary.<\/p>\n

If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.<\/p>\n

Look at the two figures.<\/p>\n

\"A
\n\u24d0 Which figure looks like it has the larger area? Which looks like it has the larger perimeter?
\n\u24d1 Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?<\/p>\n

Answers will vary.<\/p>\n

The length of a rectangle is [latex]5[\/latex] feet more than the width. The area is [latex]50[\/latex] square feet. Find the length and the width.
\n\u24d0 Write the equation you would use to solve the problem.
\n\u24d1 Why can\u2019t you solve this equation with the methods you learned in the previous chapter?<\/p>\n

Self Check<\/h2>\n

\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

\".\"
\n\u24d1 On a scale of 1\u201310, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?<\/p>\n

<\/h2>\n

Solve Geometry Applications: Circles and Irregular Figures<\/h2>\n

Use Properties of Circles<\/strong>
\nIn the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.<\/strong><\/p>\n

A circular mosaic has radius [latex]3[\/latex] meters. Find the \u24d0 circumference \u24d1 area of the mosaic.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 18.84 m
\n\u24d1 28.26 sq. m<\/div>\n<\/div>\n

A circular fountain has radius [latex]8[\/latex] feet. Find the\u00a0<\/span>\u24d0 circumference \u24d1 area of the fountain.<\/p>\n

Find the diameter of a circle with circumference [latex]150.72[\/latex] inches.<\/p>\n

Show Solution<\/span><\/p>\n
48 in.<\/div>\n<\/div>\n

Find the radius of a circle with circumference [latex]345.4[\/latex] centimeters<\/p>\n

Find the Area of Irregular Figures<\/strong>
\nIn the following exercises, find the area of each shaded region.<\/strong><\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
30 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
300 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
199.25 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

Solve Geometry Applications: Volume and Surface Area<\/h2>\n

Find Volume and Surface Area of Rectangular Solids<\/strong>
\nIn the following exercises, find the \u24d0 volume \u24d1 surface area of the rectangular solid.<\/strong><\/p>\n

a rectangular solid with length [latex]14[\/latex] centimeters, width [latex]4.5[\/latex] centimeters, and height [latex]10[\/latex] centimeters<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 630 cu. cm
\n\u24d1 496 sq. cm<\/div>\n<\/div>\n

a cube with sides that are [latex]3[\/latex] feet long<\/p>\n

a cube of tofu with sides [latex]2.5[\/latex] inches<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 15.625 cu. in.
\n\u24d1 37.5 sq. in.<\/div>\n<\/div>\n

a rectangular carton with length [latex]32[\/latex] inches, width [latex]18[\/latex] inches, and height [latex]10[\/latex] inches<\/p>\n

Find Volume and Surface Area of Spheres<\/strong>
\nIn the following exercises, find the \u24d0 volume \u24d1 surface area of the sphere.<\/strong><\/p>\n

a sphere with radius [latex]4[\/latex] yards<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 267.95 cu. yd.
\n\u24d1 200.96 sq. yd.<\/div>\n<\/div>\n

a sphere with radius [latex]12[\/latex] meters<\/p>\n

a baseball with radius [latex]1.45[\/latex] inches<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 12.76 cu. in.
\n\u24d1 26.41 sq. in.<\/div>\n<\/div>\n

a soccer ball with radius [latex]22[\/latex] centimeters<\/p>\n

Find Volume and Surface Area of Cylinders<\/strong>
\nIn the following exercises, find the \u24d0 volume \u24d1 surface area of the cylinder.<\/strong><\/p>\n

a cylinder with radius [latex]2[\/latex] yards and height [latex]6[\/latex] yards<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 75.36 cu. yd.
\n\u24d1 100.48 sq. yd.<\/div>\n<\/div>\n

a cylinder with diameter [latex]18[\/latex] inches and height [latex]40[\/latex] inches<\/p>\n

a juice can with diameter [latex]8[\/latex] centimeters and height [latex]15[\/latex] centimeters<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 753.6 cu. cm
\n\u24d1 477.28 sq. cm<\/div>\n<\/div>\n

a cylindrical pylon with diameter [latex]0.8[\/latex] feet and height [latex]2.5[\/latex] feet<\/p>\n

Find Volume of Cones<\/strong>
\nIn the following exercises, find the volume of the cone.<\/strong><\/p>\n

a cone with height [latex]5[\/latex] meters and radius [latex]1[\/latex] meter<\/p>\n

Show Solution<\/span><\/p>\n
5.233 cu. m<\/div>\n<\/div>\n

a cone with height [latex]24[\/latex] feet and radius [latex]8[\/latex] feet<\/p>\n

a cone-shaped water cup with diameter [latex]2.6[\/latex] inches and height [latex]2.6[\/latex] inches<\/p>\n

Show Solution<\/span><\/p>\n
4.599 cu. in.<\/div>\n<\/div>\n

a cone-shaped pile of gravel with diameter [latex]6[\/latex] yards and height [latex]5[\/latex] yards<\/p>\n

Mixed Practice<\/h2>\n

Find the complement of a [latex]{52^\\circ }[\/latex] angle.<\/p>\n

Show Solution<\/span><\/p>\n
38\u00b0<\/div>\n<\/div>\n

The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is [latex]14[\/latex] more than the measure of the smallest angle. Find the measures of all three angles.<\/p>\n

The perimeter of an equilateral triangle is [latex]145[\/latex] feet. Find the length of each side.<\/p>\n

Show Solution<\/span><\/p>\n
48.3<\/div>\n<\/div>\n

[latex]\\Delta ABC[\/latex] is similar to [latex]\\Delta XYZ[\/latex]. Find the length of side [latex]c[\/latex].<\/p>\n

\"Two<\/p>\n

Find the length of the missing side. Round to the nearest tenth, if necessary.<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
10<\/div>\n<\/div>\n

Find the length of the missing side. Round to the nearest tenth, if necessary.<\/p>\n

\"A<\/p>\n

A baseball diamond is shaped like a square with sides [latex]90[\/latex] feet long. How far is it from home plate to second base, as shown?<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
127.3 ft<\/div>\n<\/div>\n

The length of a rectangle is [latex]2[\/latex] feet more than five times the width. The perimeter is [latex]40[\/latex] feet. Find the dimensions of the rectangle.<\/p>\n

A triangular poster has base [latex]80[\/latex] centimeters and height [latex]55[\/latex] centimeters. Find the area of the poster.<\/p>\n

Show Solution<\/span><\/p>\n
2200 square centimeters<\/div>\n<\/div>\n

A trapezoid has height [latex]14[\/latex] inches and bases [latex]20[\/latex] inches and [latex]23[\/latex] inches. Find the area of the trapezoid.<\/p>\n

A circular pool has diameter [latex]90[\/latex] inches. What is its circumference? Round to the nearest tenth.<\/em><\/p>\n

Show Solution<\/span><\/p>\n
282.6 inches<\/div>\n<\/div>\n

Find the area of the shaded region. Round to the nearest tenth.<\/p>\n

\"A<\/p>\n

Find the volume of a rectangular room with width [latex]12[\/latex] feet, length [latex]15[\/latex] feet, and height [latex]8[\/latex] feet.<\/p>\n

Show Solution<\/span><\/p>\n
1440<\/div>\n<\/div>\n

A coffee can is shaped like a cylinder with height [latex]7[\/latex] inches and radius [latex]5[\/latex] inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth.<\/p>\n

A traffic cone has height [latex]75[\/latex] centimeters. The radius of the base is [latex]20[\/latex] centimeters. Find the volume of the cone. Round to the nearest tenth.<\/p>\n

Show Solution<\/span><\/p>\n
31,400 cubic inches<\/div>\n<\/div>\n

Solve the formula [latex]A=\\Large\\frac{1}{2}\\normalsize bh[\/latex] for [latex]h\\text{:}[\/latex] \u24d0 when [latex]A=1716[\/latex] and [latex]b=66[\/latex] \u24d1 in general.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 [latex]\\text{height}=52[\/latex]
\n\u24d1 [latex]h=\\Large\\frac{2A}{b}[\/latex]<\/div>\n<\/div>\n

Solve [latex]x+5y=14[\/latex] for [latex]y[\/latex].<\/p>\n

Practice Makes Perfect<\/h2>\n

Use the Properties of Circles<\/strong>
\nIn the following exercises, solve using the properties of circles.<\/p>\n

The lid of a paint bucket is a circle with radius [latex]7[\/latex] inches. Find the \u24d0 circumference and \u24d1 area of the lid.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 43.96 in.
\n\u24d1 153.86 sq. in.<\/div>\n<\/div>\n

An extra-large pizza is a circle with radius [latex]8[\/latex] inches. Find the \u24d0 circumference and \u24d1 area of the pizza.<\/p>\n

A farm sprinkler spreads water in a circle with radius of [latex]8.5[\/latex] feet. Find the \u24d0 circumference and \u24d1 area of the watered circle.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 53.38 ft
\n\u24d1 226.865 sq. ft<\/div>\n<\/div>\n

A circular rug has radius of [latex]3.5[\/latex] feet. Find the \u24d0 circumference and \u24d1 area of the rug.<\/p>\n

A reflecting pool is in the shape of a circle with diameter of [latex]20[\/latex] feet. What is the circumference of the pool?<\/p>\n

Show Solution<\/span><\/p>\n
62.8 ft<\/div>\n<\/div>\n

A turntable is a circle with diameter of [latex]10[\/latex] inches. What is the circumference of the turntable?<\/p>\n

A circular saw has a diameter of [latex]12[\/latex] inches. What is the circumference of the saw?<\/p>\n

Show Solution<\/span><\/p>\n
37.68 in.<\/div>\n<\/div>\n

A round coin has a diameter of [latex]3[\/latex] centimeters. What is the circumference of the coin?<\/p>\n

A barbecue grill is a circle with a diameter of [latex]2.2[\/latex] feet. What is the circumference of the grill?<\/p>\n

Show Solution<\/span><\/p>\n
6.908 ft<\/div>\n<\/div>\n

The top of a pie tin is a circle with a diameter of [latex]9.5[\/latex] inches. What is the circumference of the top?<\/p>\n

A circle has a circumference of [latex]163.28[\/latex] inches. Find the diameter.<\/p>\n

Show Solution<\/span><\/p>\n
52 in.<\/div>\n<\/div>\n

A circle has a circumference of [latex]59.66[\/latex] feet. Find the diameter.<\/p>\n

A circle has a circumference of [latex]17.27[\/latex] meters. Find the diameter.<\/p>\n

Show Solution<\/span><\/p>\n
5.5 m<\/div>\n<\/div>\n

A circle has a circumference of [latex]80.07[\/latex] centimeters. Find the diameter.<\/p>\n

In the following exercises, find the radius of the circle with given circumference.<\/strong><\/p>\n

A circle has a circumference of [latex]150.72[\/latex] feet.<\/p>\n

Show Solution<\/span><\/p>\n
24 ft<\/div>\n<\/div>\n

A circle has a circumference of [latex]251.2[\/latex] centimeters.<\/p>\n

A circle has a circumference of [latex]40.82[\/latex] miles.<\/p>\n

Show Solution<\/span><\/p>\n
6.5 mi<\/div>\n<\/div>\n

A circle has a circumference of [latex]78.5[\/latex] inches.<\/p>\n

Find the Area of Irregular Figures<\/strong>
\nIn the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
16 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
30 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
57.5 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"Two<\/p>\n

Show Solution<\/span><\/p>\n
12 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
67.5 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
89 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
44.81 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
41.12 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
35.13 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
95.625 sq. units<\/div>\n<\/div>\n

\"A<\/p>\n

In the following exercises, solve.<\/strong><\/p>\n

A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides [latex]250[\/latex] feet long, and the triangles are isosceles right triangles. Find the area of the park.<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
187,500 sq. ft<\/div>\n<\/div>\n

A gift box will be made from a rectangular piece of cardboard measuring [latex]12[\/latex] inches by [latex]20[\/latex] inches, with squares cut out of the corners of the sides, as shown. The sides of the squares are [latex]3[\/latex] inches. Find the area of the cardboard after the corners are cut out.<\/p>\n

\"A<\/p>\n

Perry needs to put in a new lawn. His lot is a rectangle with a length of [latex]120[\/latex] feet and a width of [latex]100[\/latex] feet. The house is rectangular and measures [latex]50[\/latex] feet by [latex]40[\/latex] feet. His driveway is rectangular and measures [latex]20[\/latex] feet by [latex]30[\/latex] feet, as shown. Find the area of Perry\u2019s lawn.<\/p>\n

\"A<\/p>\n

Show Solution<\/span><\/p>\n
9400 sq. ft<\/div>\n<\/div>\n

Denise is planning to put a deck in her back yard. The deck will be a [latex]\\text{20-ft}[\/latex] by [latex]\\text{12-ft}[\/latex] rectangle with a semicircle of diameter [latex]6[\/latex] feet, as shown below. Find the area of the deck.<\/span><\/p>\n

\"A<\/p>\n

Everyday Math<\/h2>\n

Area of a Tabletop<\/strong> Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a [latex]\\text{1-ft}[\/latex] by [latex]\\text{3-ft}[\/latex] rectangle with a semicircle at each end, as shown. \u24d0 Find the area of the table with one leaf up. \u24d1 Find the area of the table with both leaves up.<\/p>\n

\"An<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 6.5325 sq. ft
\n\u24d1 10.065 sq. ft<\/div>\n<\/div>\n

Painting<\/strong> Leora wants to paint the nursery in her house. The nursery is an [latex]\\text{8-ft}[\/latex] by [latex]\\text{10-ft}[\/latex] rectangle, and the ceiling is [latex]8[\/latex] feet tall. There is a [latex]\\text{3-ft}[\/latex] by [latex]\\text{6.5-ft}[\/latex] door on one wall, a [latex]\\text{3-ft}[\/latex] by [latex]\\text{6.5-ft}[\/latex] closet door on another wall, and one [latex]\\text{4-ft}[\/latex] by [latex]\\text{3.5-ft}[\/latex] window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?<\/p>\n

Writing Exercises<\/h2>\n

Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.<\/p>\n

\"A<\/p>\n

Answers will vary.<\/p>\n

A circle has a diameter of [latex]14[\/latex] feet. Find the area of the circle \u24d0 using [latex]3.14[\/latex] for [latex]\\pi[\/latex] \u24d1 using [latex]\\Large\\frac{22}{7}[\/latex] for [latex]\\text{\\pi }[\/latex]. \u24d2 Which calculation to do prefer? Why?<\/p>\n

Self Check<\/h2>\n

\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

\".\"
\n\u24d1 After looking at the checklist, do you think you are well prepared for the next section? Why or why not?<\/p>\n

<\/h2>\n

Practice Makes Perfect<\/h2>\n

Find Volume and Surface Area of Rectangular Solids<\/strong>
\nIn the following exercises, find \u24d0 the volume and \u24d1 the surface area of the rectangular solid with the given dimensions.<\/strong><\/p>\n

length [latex]2[\/latex] meters, width [latex]1.5[\/latex] meters, height [latex]3[\/latex] meters<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 9 cu. m
\n\u24d1 27 sq. m<\/div>\n<\/div>\n

length [latex]5[\/latex] feet, width [latex]8[\/latex] feet, height [latex]2.5[\/latex] feet<\/p>\n

length [latex]3.5[\/latex] yards, width [latex]2.1[\/latex] yards, height [latex]2.4[\/latex] yards<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 17.64 cu. yd.
\n\u24d1 41.58 sq. yd.<\/div>\n<\/div>\n

length [latex]8.8[\/latex] centimeters, width [latex]6.5[\/latex] centimeters, height [latex]4.2[\/latex] centimeters<\/p>\n

In the following exercises, solve.<\/strong><\/p>\n

Moving van<\/strong> A rectangular moving van has length [latex]16[\/latex] feet, width [latex]8[\/latex] feet, and height [latex]8[\/latex] feet. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 1,024 cu. ft
\n\u24d1 640 sq. ft<\/div>\n<\/div>\n

Gift box<\/strong> A rectangular gift box has length [latex]26[\/latex] inches, width [latex]16[\/latex] inches, and height [latex]4[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Carton<\/strong> A rectangular carton has length
\n[latex]21.3[\/latex] cm, width [latex]24.2[\/latex] cm, and height [latex]6.5[\/latex] cm. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 3,350.49 cu. cm
\n\u24d1 1,622.42 sq. cm<\/div>\n<\/div>\n

Shipping container<\/strong> A rectangular shipping container has length [latex]22.8[\/latex] feet, width [latex]8.5[\/latex] feet, and height [latex]8.2[\/latex] feet. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

In the following exercises, find \u24d0 the volume and \u24d1 the surface area of the cube with the given side length.<\/strong><\/p>\n

[latex]5[\/latex] centimeters<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 125 cu. cm
\n\u24d1 150 sq. cm<\/div>\n<\/div>\n

[latex]6[\/latex] inches<\/p>\n

[latex]10.4[\/latex] feet<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 1124.864 cu. ft.
\n\u24d1 648.96 sq. ft<\/div>\n<\/div>\n

[latex]12.5[\/latex] meters<\/p>\n

In the following exercises, solve.<\/strong><\/p>\n

Science center<\/strong> Each side of the cube at the Discovery Science Center in Santa Ana is [latex]64[\/latex] feet long. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 262,144 cu. ft
\n\u24d1 24,576 sq. ft<\/div>\n<\/div>\n

Museum<\/strong> A cube-shaped museum has sides [latex]45[\/latex] meters long. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Base of statue<\/strong> The base of a statue is a cube with sides [latex]2.8[\/latex] meters long. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 21.952 cu. m
\n\u24d1 47.04 sq. m<\/div>\n<\/div>\n

Tissue box<\/strong> A box of tissues is a cube with sides 4.5 inches long. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Find the Volume and Surface Area of Spheres<\/strong><\/p>\n

In the following exercises, find \u24d0 the volume and \u24d1 the surface area of the sphere with the given radius. Round answers to the nearest hundredth.<\/strong><\/p>\n

[latex]3[\/latex] centimeters<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 113.04 cu. cm
\n\u24d1 113.04 sq. cm<\/div>\n<\/div>\n

[latex]9[\/latex] inches<\/p>\n

[latex]7.5[\/latex] feet<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 1,766.25 cu. ft
\n\u24d1 706.5 sq. ft <\/div>\n<\/div>\n

[latex]2.1[\/latex] yards<\/p>\n

In the following exercises, solve. Round answers to the nearest hundredth.<\/strong><\/p>\n

Exercise ball<\/strong> An exercise ball has a radius of [latex]15[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 14,130 cu. in.
\n\u24d1 2,826 sq. in.<\/div>\n<\/div>\n

Balloon ride<\/strong> The Great Park Balloon is a big orange sphere with a radius of [latex]36[\/latex] feet . Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Golf ball<\/strong> A golf ball has a radius of [latex]4.5[\/latex] centimeters. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 381.51 cu. cm
\n\u24d1 254.34 sq. cm<\/div>\n<\/div>\n

Baseball<\/strong> A baseball has a radius of [latex]2.9[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Find the Volume and Surface Area of a Cylinder<\/strong>
\nIn the following exercises, find \u24d0 the volume and \u24d1 the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.<\/strong><\/p>\n

radius [latex]3[\/latex] feet, height [latex]9[\/latex] feet<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 254.34 cu. ft
\n\u24d1 226.08 sq. ft<\/div>\n<\/div>\n

radius [latex]5[\/latex] centimeters, height [latex]15[\/latex] centimeters<\/p>\n

radius [latex]1.5[\/latex] meters, height [latex]4.2[\/latex] meters<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 29.673 cu. m
\n\u24d1 53.694 sq. m<\/div>\n<\/div>\n

radius [latex]1.3[\/latex] yards, height [latex]2.8[\/latex] yards<\/p>\n

In the following exercises, solve. Round answers to the nearest hundredth.<\/strong><\/p>\n

Coffee can<\/strong> A can of coffee has a radius of [latex]5[\/latex] cm and a height of [latex]13[\/latex] cm. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 1,020.5 cu. cm
\n\u24d1 565.2 sq. cm<\/div>\n<\/div>\n

Snack pack<\/strong> A snack pack of cookies is shaped like a cylinder with radius [latex]4[\/latex] cm and height [latex]3[\/latex] cm. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Barber shop pole<\/strong> A cylindrical barber shop pole has a diameter of [latex]6[\/latex] inches and height of [latex]24[\/latex] inches. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 678.24 cu. in.
\n\u24d1 508.68 sq. in.<\/div>\n<\/div>\n

Architecture<\/strong> A cylindrical column has a diameter of [latex]8[\/latex] feet and a height of [latex]28[\/latex] feet. Find its \u24d0 volume and \u24d1 surface area.<\/p>\n

Find the Volume of Cones<\/strong>
\nIn the following exercises, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.<\/strong><\/p>\n

height [latex]9[\/latex] feet and radius [latex]2[\/latex] feet<\/p>\n

Show Solution<\/span><\/p>\n
37.68 cu. ft<\/div>\n<\/div>\n

height [latex]8[\/latex] inches and radius [latex]6[\/latex] inches<\/p>\n

height [latex]12.4[\/latex] centimeters and radius [latex]5[\/latex] cm<\/p>\n

Show Solution<\/span><\/p>\n
324.47 cu. cm<\/div>\n<\/div>\n

height [latex]15.2[\/latex] meters and radius [latex]4[\/latex] meters<\/p>\n

In the following exercises, solve. Round answers to the nearest hundredth.<\/strong><\/p>\n

Teepee<\/strong> What is the volume of a cone-shaped tee-pee tent that is [latex]10[\/latex] feet tall and [latex]10[\/latex] feet across at the base?<\/p>\n

Show Solution<\/span><\/p>\n
261.67 cu. ft<\/div>\n<\/div>\n

Popcorn cup<\/strong> What is the volume of a cone-shaped popcorn cup that is [latex]8[\/latex] inches tall and [latex]6[\/latex] inches across at the base?<\/p>\n

Silo<\/strong> What is the volume of a cone-shaped silo that is [latex]50[\/latex] feet tall and [latex]70[\/latex] feet across at the base?<\/p>\n

Show Solution<\/span><\/p>\n
64,108.33 cu. ft<\/div>\n<\/div>\n

Sand pile<\/strong> What is the volume of a cone-shaped pile of sand that is [latex]12[\/latex] meters tall and [latex]30[\/latex] meters across at the base?<\/p>\n

Everyday Math<\/h2>\n

Street light post<\/strong> The post of a street light is shaped like a truncated cone, as shown in the picture below. It is a large cone minus a smaller top cone. The large cone is [latex]30[\/latex] feet tall with base radius [latex]1[\/latex] foot. The smaller cone is [latex]10[\/latex] feet tall with base radius of [latex]0.5[\/latex] feet. To the nearest tenth,
\n\u24d0 find the volume of the large cone.
\n\u24d1 find the volume of the small cone.
\n\u24d2 find the volume of the post by subtracting the volume of the small cone from the volume of the large cone.<\/p>\n

\"An<\/p>\n

Show Solution<\/span><\/p>\n
\u24d0 31.4 cu. ft
\n\u24d1 2.6 cu. ft
\n\u24d2 28.8 cu. ft<\/div>\n<\/div>\n

Ice cream cones<\/strong> A regular ice cream cone is 4 inches tall and has a diameter of [latex]2.5[\/latex] inches. A waffle cone is [latex]7[\/latex] inches tall and has a diameter of [latex]3.25[\/latex] inches. To the nearest hundredth,
\n\u24d0 find the volume of the regular ice cream cone.
\n\u24d1 find the volume of the waffle cone.
\n\u24d2 how much more ice cream fits in the waffle cone compared to the regular cone?<\/p>\n

Writing Exercises<\/h2>\n

The formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape.<\/p>\n

Answers will vary.<\/p>\n

Which has a larger volume, a cube of sides of [latex]8[\/latex] feet or a sphere with a diameter of [latex]8[\/latex] feet? Explain your reasoning.<\/p>\n

Self Check<\/h2>\n

\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

\".\"
\n\u24d1 After reviewing this checklist, what will you do to become confident for all objectives?<\/p>\n

<\/h2>\n

Practice Makes Perfect<\/h2>\n

Make Unit Conversions in the U.S. System<\/strong>
\nIn the following exercises, convert the units.<\/strong><\/p>\n

A park bench is [latex]6[\/latex] feet long. Convert the length to inches.<\/p>\n

A floor tile is [latex]2[\/latex] feet wide. Convert the width to inches.<\/p>\n

Show Solution<\/span><\/p>\n
24 inches<\/div>\n<\/div>\n

A ribbon is [latex]18[\/latex] inches long. Convert the length to feet.<\/p>\n

Carson is [latex]45[\/latex] inches tall. Convert his height to feet.<\/p>\n

Show Solution<\/span><\/p>\n
3.75 feet<\/div>\n<\/div>\n

Jon is [latex]6[\/latex] feet [latex]4[\/latex] inches tall. Convert his height to inches.<\/p>\n

Faye is [latex]4[\/latex] feet [latex]10[\/latex] inches tall. Convert her height to inches.<\/p>\n

Show Solution<\/span><\/p>\n
58 inches<\/div>\n<\/div>\n

A football field is [latex]160[\/latex] feet wide. Convert the width to yards.<\/p>\n

On a baseball diamond, the distance from home plate to first base is [latex]30[\/latex] yards. Convert the distance to feet.<\/p>\n

Show Solution<\/span><\/p>\n
90 feet<\/div>\n<\/div>\n

Ulises lives [latex]1.5[\/latex] miles from school. Convert the distance to feet.<\/p>\n

Denver, Colorado, is [latex]5,183[\/latex] feet above sea level. Convert the height to miles.<\/p>\n

Show Solution<\/span><\/p>\n
0.98 miles<\/div>\n<\/div>\n

A killer whale weighs [latex]4.6[\/latex] tons. Convert the weight to pounds.<\/p>\n

Blue whales can weigh as much as [latex]150[\/latex] tons. Convert the weight to pounds.<\/p>\n

Show Solution<\/span><\/p>\n
300,000 pounds<\/div>\n<\/div>\n

An empty bus weighs [latex]35,000[\/latex] pounds. Convert the weight to tons.<\/p>\n

At take-off, an airplane weighs [latex]220,000[\/latex] pounds. Convert the weight to tons.<\/p>\n

Show Solution<\/span><\/p>\n
110 tons<\/div>\n<\/div>\n

The voyage of the Mayflower<\/em> took [latex]2[\/latex] months and [latex]5[\/latex] days. Convert the time to days.<\/p>\n

Lynn\u2019s cruise lasted [latex]6[\/latex] days and [latex]18[\/latex] hours. Convert the time to hours.<\/p>\n

Show Solution<\/span><\/p>\n
162 hours<\/div>\n<\/div>\n

Rocco waited [latex]1\\Large\\frac{1}{2}[\/latex] hours for his appointment. Convert the time to seconds.<\/p>\n

Misty\u2019s surgery lasted [latex]2\\Large\\frac{1}{4}[\/latex] hours. Convert the time to seconds.<\/p>\n

Show Solution<\/span><\/p>\n
8100 seconds<\/div>\n<\/div>\n

How many teaspoons are in a pint?<\/p>\n

How many tablespoons are in a gallon?<\/p>\n

Show Solution<\/span><\/p>\n
256 tablespoons<\/div>\n<\/div>\n

JJ\u2019s cat, Posy, weighs [latex]14[\/latex] pounds. Convert her weight to ounces.<\/p>\n

April\u2019s dog, Beans, weighs [latex]8[\/latex] pounds. Convert his weight to ounces.<\/p>\n

Show Solution<\/span><\/p>\n
128 ounces<\/div>\n<\/div>\n

Baby Preston weighed [latex]7[\/latex] pounds [latex]3[\/latex] ounces at birth. Convert his weight to ounces.<\/p>\n

Baby Audrey weighed [latex]6[\/latex] pounds [latex]15[\/latex] ounces at birth. Convert her weight to ounces.<\/p>\n

Show Solution<\/span><\/p>\n
111 ounces<\/div>\n<\/div>\n

Crista will serve [latex]20[\/latex] cups of juice at her son\u2019s party. Convert the volume to gallons.<\/p>\n

Lance needs [latex]500[\/latex] cups of water for the runners in a race. Convert the volume to gallons.<\/p>\n

Show Solution<\/span><\/p>\n
31.25 gallons<\/div>\n<\/div>\n

Use Mixed Units of Measurement in the U.S. System<\/strong>
\nIn the following exercises, solve and write your answer in mixed units.<\/strong><\/p>\n

Eli caught three fish. The weights of the fish were [latex]2[\/latex] pounds [latex]4[\/latex] ounces, [latex]1[\/latex] pound [latex]11[\/latex] ounces, and [latex]4[\/latex] pounds [latex]14[\/latex] ounces. What was the total weight of the three fish?<\/p>\n

Judy bought [latex]1[\/latex] pound [latex]6[\/latex] ounces of almonds, [latex]2[\/latex] pounds [latex]3[\/latex] ounces of walnuts, and [latex]8[\/latex] ounces of cashews. What was the total weight of the nuts?<\/p>\n

Show Solution<\/span><\/p>\n
4 lbs. 1 oz.<\/div>\n<\/div>\n

One day Anya kept track of the number of minutes she spent driving. She recorded trips of [latex]45,10,8,65,20,\\text{and 35 minutes.}[\/latex] How much time (in hours and minutes) did Anya spend driving?<\/p>\n

Last year Eric went on [latex]6[\/latex] business trips. The number of days of each was [latex]5,2,8,12,6,\\text{and 3.}[\/latex] How much time (in weeks and days) did Eric spend on business trips last year?<\/p>\n

Show Solution<\/span><\/p>\n
5 weeks and 1 day<\/div>\n<\/div>\n

Renee attached a [latex]\\text{6-foot - 6-inch}[\/latex] extension cord to her computer\u2019s [latex]\\text{3-foot - 8-inch}[\/latex] power cord. What was the total length of the cords?<\/p>\n

Fawzi\u2019s SUV is [latex]6[\/latex] feet [latex]4[\/latex] inches tall. If he puts a [latex]\\text{2-foot - 10-inch}[\/latex] box on top of his SUV, what is the total height of the SUV and the box?<\/p>\n

Show Solution<\/span><\/p>\n
9 ft 2 in<\/div>\n<\/div>\n

Leilani wants to make [latex]8[\/latex] placemats. For each placemat she needs [latex]18[\/latex] inches of fabric. How many yards of fabric will she need for the [latex]8[\/latex] placemats?<\/p>\n

Mireille needs to cut [latex]24[\/latex] inches of ribbon for each of the [latex]12[\/latex] girls in her dance class. How many yards of ribbon will she need altogether?<\/p>\n

Show Solution<\/span><\/p>\n
8 yards<\/div>\n<\/div>\n

Make Unit Conversions in the Metric System<\/strong>
\nIn the following exercises, convert the units.<\/strong><\/p>\n

Ghalib ran [latex]5[\/latex] kilometers. Convert the length to meters.<\/p>\n

Kitaka hiked [latex]8[\/latex] kilometers. Convert the length to meters.<\/p>\n

Show Solution<\/span><\/p>\n
8000 meters<\/div>\n<\/div>\n

Estrella is [latex]1.55[\/latex] meters tall. Convert her height to centimeters.<\/p>\n

The width of the wading pool is [latex]2.45[\/latex] meters. Convert the width to centimeters.<\/p>\n

Show Solution<\/span><\/p>\n
245 centimeters<\/div>\n<\/div>\n

Mount Whitney is [latex]3,072[\/latex] meters tall. Convert the height to kilometers.<\/p>\n

The depth of the Mariana Trench is [latex]10,911[\/latex] meters. Convert the depth to kilometers.<\/p>\n

Show Solution<\/span><\/p>\n
10.911 kilometers<\/div>\n<\/div>\n

June\u2019s multivitamin contains [latex]1,500[\/latex] milligrams of calcium. Convert this to grams.<\/p>\n

A typical ruby-throated hummingbird weights [latex]3[\/latex] grams. Convert this to milligrams.<\/p>\n

Show Solution<\/span><\/p>\n
3000 milligrams<\/div>\n<\/div>\n

One stick of butter contains [latex]91.6[\/latex] grams of fat. Convert this to milligrams.<\/p>\n

One serving of gourmet ice cream has [latex]25[\/latex] grams of fat. Convert this to milligrams.<\/p>\n

Show Solution<\/span><\/p>\n
25,000 milligrams<\/div>\n<\/div>\n

The maximum mass of an airmail letter is [latex]2[\/latex] kilograms. Convert this to grams.<\/p>\n

Dimitri\u2019s daughter weighed [latex]3.8[\/latex] kilograms at birth. Convert this to grams.<\/p>\n

Show Solution<\/span><\/p>\n
3800 grams<\/div>\n<\/div>\n

A bottle of wine contained [latex]750[\/latex] milliliters. Convert this to liters.<\/p>\n

A bottle of medicine contained [latex]300[\/latex] milliliters. Convert this to liters.<\/p>\n

Show Solution<\/span><\/p>\n
0.3 liters<\/div>\n<\/div>\n

Use Mixed Units of Measurement in the Metric System<\/strong>
\nIn the following exercises, solve and write your answer in mixed units.<\/strong><\/p>\n

Matthias is [latex]1.8[\/latex] meters tall. His son is [latex]89[\/latex] centimeters tall. How much taller, in centimeters, is Matthias than his son?<\/p>\n

Stavros is [latex]1.6[\/latex] meters tall. His sister is [latex]95[\/latex] centimeters tall. How much taller, in centimeters, is Stavros than his sister?<\/p>\n

Show Solution<\/span><\/p>\n
65 centimeters<\/div>\n<\/div>\n

A typical dove weighs [latex]345[\/latex] grams. A typical duck weighs [latex]1.2[\/latex] kilograms. What is the difference, in grams, of the weights of a duck and a dove?<\/p>\n

Concetta had a [latex]\\text{2-kilogram}[\/latex] bag of flour. She used [latex]180[\/latex] grams of flour to make biscotti. How many kilograms of flour are left in the bag?<\/p>\n

Show Solution<\/span><\/p>\n
1.82 kilograms<\/div>\n<\/div>\n

Harry mailed [latex]5[\/latex] packages that weighed [latex]420[\/latex] grams each. What was the total weight of the packages in kilograms?<\/p>\n

One glass of orange juice provides [latex]560[\/latex] milligrams of potassium. Linda drinks one glass of orange juice every morning. How many grams of potassium does Linda get from her orange juice in [latex]30[\/latex] days?<\/p>\n

Show Solution<\/span><\/p>\n
16.8 grams<\/div>\n<\/div>\n

Jonas drinks [latex]200[\/latex] milliliters of water [latex]8[\/latex] times a day. How many liters of water does Jonas drink in a day?<\/p>\n

One serving of whole grain sandwich bread provides [latex]6[\/latex] grams of protein. How many milligrams of protein are provided by [latex]7[\/latex] servings of whole grain sandwich bread?<\/p>\n

Show Solution<\/span><\/p>\n
42,000 milligrams<\/div>\n<\/div>\n

Convert Between U.S. and Metric Systems<\/strong>
\nIn the following exercises, make the unit conversions. Round to the nearest tenth.<\/strong><\/p>\n

Bill is [latex]75[\/latex] inches tall. Convert his height to centimeters.<\/p>\n

Frankie is [latex]42[\/latex] inches tall. Convert his height to centimeters.<\/p>\n

Show Solution<\/span><\/p>\n
106.7 centimeters<\/div>\n<\/div>\n

Marcus passed a football [latex]24[\/latex] yards. Convert the pass length to meters.<\/p>\n

Connie bought [latex]9[\/latex] yards of fabric to make drapes. Convert the fabric length to meters.<\/p>\n

Show Solution<\/span><\/p>\n
8.2 meters<\/div>\n<\/div>\n

Each American throws out an average of [latex]1,650[\/latex] pounds of garbage per year. Convert this weight to kilograms.<\/p>\n

An average American will throw away [latex]90,000[\/latex] pounds of trash over his or her lifetime. Convert this weight to kilograms.<\/p>\n

Show Solution<\/span><\/p>\n
41,500 kilograms<\/div>\n<\/div>\n

A [latex]\\text{5K}[\/latex] run is [latex]5[\/latex] kilometers long. Convert this length to miles.<\/p>\n

Kathryn is [latex]1.6[\/latex] meters tall. Convert her height to feet.<\/p>\n

Show Solution<\/span><\/p>\n
5.2 feet<\/div>\n<\/div>\n

Dawn\u2019s suitcase weighed [latex]20[\/latex] kilograms. Convert the weight to pounds.<\/p>\n

Jackson\u2019s backpack weighs [latex]15[\/latex] kilograms. Convert the weight to pounds.<\/p>\n

Show Solution<\/span><\/p>\n
33 pounds<\/div>\n<\/div>\n

Ozzie put [latex]14[\/latex] gallons of gas in his truck. Convert the volume to liters.<\/p>\n

Bernard bought [latex]8[\/latex] gallons of paint. Convert the volume to liters.<\/p>\n

Show Solution<\/span><\/p>\n
30.4 liters<\/div>\n<\/div>\n

Convert between Fahrenheit and Celsius<\/strong>
\nIn the following exercises, convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth.<\/p>\n

[latex]86{^\\circ F}[\/latex]<\/p>\n

[latex]77{^\\circ F}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
25\u00b0C<\/div>\n<\/div>\n

[latex]104{^\\circ F}[\/latex]<\/p>\n

[latex]14{^\\circ F}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
\u221210\u00b0C<\/div>\n<\/div>\n

[latex]72{^\\circ F}[\/latex]<\/p>\n

[latex]4{^\\circ F}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
\u221215.5\u00b0C<\/div>\n<\/div>\n

[latex]0{^\\circ F}[\/latex]<\/p>\n

[latex]120{^\\circ F}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
48.9\u00b0C<\/div>\n<\/div>\n

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.<\/strong><\/p>\n

[latex]5{^\\circ C}[\/latex]<\/p>\n

[latex]25{^\\circ C}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
77\u00b0F<\/div>\n<\/div>\n

[latex]-10{^\\circ C}[\/latex]<\/p>\n

[latex]-15{^\\circ C}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
5\u00b0F<\/div>\n<\/div>\n

[latex]22{^\\circ C}[\/latex]<\/p>\n

[latex]8{^\\circ C}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
46.4\u00b0F<\/div>\n<\/div>\n

[latex]43{^\\circ C}[\/latex]<\/p>\n

[latex]16{^\\circ C}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
60.8\u00b0F<\/div>\n<\/div>\n

Everyday Math<\/h2>\n

Nutrition<\/strong> Julian drinks one can of soda every day. Each can of soda contains [latex]40[\/latex] grams of sugar. How many kilograms of sugar does Julian get from soda in [latex]1[\/latex] year?<\/p>\n

Reflectors<\/strong> The reflectors in each lane-marking stripe on a highway are spaced [latex]16[\/latex] yards apart. How many reflectors are needed for a one-mile-long stretch of highway?<\/p>\n

Show Solution<\/span><\/p>\n
110 reflectors<\/div>\n<\/div>\n

Writing Exercises<\/h2>\n

Some people think that [latex]65{^\\circ }[\/latex] to [latex]75{^\\circ }[\/latex] Fahrenheit is the ideal temperature range.
\n\u24d0 What is your ideal temperature range? Why do you think so?
\n\u24d1 Convert your ideal temperatures from Fahrenheit to Celsius.<\/p>\n

\u24d0 Did you grow up using the U.S. customary or the metric system of measurement? \u24d1 Describe two examples in your life when you had to convert between systems of measurement. \u24d2 Which system do you think is easier to use? Explain.<\/p>\n

Self Check<\/h2>\n

\u24d0 After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n

\".\"
\n\u24d1 Overall, after looking at the checklist, do you think you are well-prepared for the next chapter? Why or why not?<\/p>\n

Systems of Measurement<\/h2>\n

In the following exercises, convert between U.S. units. Round to the nearest tenth.<\/strong><\/p>\n

A floral arbor is [latex]7[\/latex] feet tall. Convert the height to inches.<\/p>\n

A picture frame is [latex]42[\/latex] inches wide. Convert the width to feet.<\/p>\n

Show Solution<\/span><\/p>\n
3.5 feet<\/div>\n<\/div>\n

Kelly is [latex]5[\/latex] feet [latex]4[\/latex] inches tall. Convert her height to inches.<\/p>\n

A playground is [latex]45[\/latex] feet wide. Convert the width to yards.<\/p>\n

Show Solution<\/span><\/p>\n
15 yards<\/div>\n<\/div>\n

The height of Mount Shasta is [latex]14,179[\/latex] feet. Convert the height to miles.<\/p>\n

Shamu weighs [latex]4.5[\/latex] tons. Convert the weight to pounds.<\/p>\n

Show Solution<\/span><\/p>\n
9000 pounds<\/div>\n<\/div>\n

The play lasted [latex]1\\Large\\frac{3}{4}[\/latex] hours. Convert the time to minutes.<\/p>\n

How many tablespoons are in a quart?<\/p>\n

Show Solution<\/span><\/p>\n
64 tablespoons<\/div>\n<\/div>\n

Naomi\u2019s baby weighed [latex]5[\/latex] pounds [latex]14[\/latex] ounces at birth. Convert the weight to ounces.<\/p>\n

Trinh needs [latex]30[\/latex] cups of paint for her class art project. Convert the volume to gallons.<\/p>\n

Show Solution<\/span><\/p>\n
1.9 gallons<\/div>\n<\/div>\n

In the following exercises, solve, and state your answer in mixed units.<\/strong><\/p>\n

John caught [latex]4[\/latex] lobsters. The weights of the lobsters were [latex]1[\/latex] pound [latex]9[\/latex] ounces, [latex]1[\/latex] pound [latex]12[\/latex] ounces, [latex]4[\/latex] pounds [latex]2[\/latex] ounces, and [latex]2[\/latex] pounds [latex]15[\/latex] ounces. What was the total weight of the lobsters?<\/p>\n

Every day last week, Pedro recorded the amount of time he spent reading. He read for [latex]50,25,83,45,32,60,\\text{and}135[\/latex] minutes. How much time, in hours and minutes, did Pedro spend reading?<\/p>\n

Show Solution<\/span><\/p>\n
7 hours 10 minutes<\/div>\n<\/div>\n

Fouad is [latex]6[\/latex] feet [latex]2[\/latex] inches tall. If he stands on a rung of a ladder [latex]8[\/latex] feet [latex]10[\/latex] inches high, how high off the ground is the top of Fouad\u2019s head?<\/p>\n

Dalila wants to make pillow covers. Each cover takes [latex]30[\/latex] inches of fabric. How many yards and inches of fabric does she need for [latex]4[\/latex] pillow covers?<\/p>\n

Show Solution<\/span><\/p>\n
3 yards, 12 inches<\/div>\n<\/div>\n

In the following exercises, convert between metric units.<\/strong><\/p>\n

Donna is [latex]1.7[\/latex] meters tall. Convert her height to centimeters.<\/p>\n

Mount Everest is [latex]8,850[\/latex] meters tall. Convert the height to kilometers.<\/p>\n

Show Solution<\/span><\/p>\n
8.85 kilometers<\/div>\n<\/div>\n

One cup of yogurt contains [latex]488[\/latex] milligrams of calcium. Convert this to grams.<\/p>\n

One cup of yogurt contains [latex]13[\/latex] grams of protein. Convert this to milligrams.<\/p>\n

Show Solution<\/span><\/p>\n
13,000 milligrams<\/div>\n<\/div>\n

Sergio weighed [latex]2.9[\/latex] kilograms at birth. Convert this to grams.<\/p>\n

A bottle of water contained [latex]650[\/latex] milliliters. Convert this to liters.<\/p>\n

Show Solution<\/span><\/p>\n
0.65 liters<\/div>\n<\/div>\n

In the following exercises, solve.<\/strong><\/p>\n

Minh is [latex]2[\/latex] meters tall. His daughter is [latex]88[\/latex] centimeters tall. How much taller, in meters, is Minh than his daughter?<\/p>\n

Selma had a [latex]\\text{1-liter}[\/latex] bottle of water. If she drank [latex]145[\/latex] milliliters, how much water, in milliliters, was left in the bottle?<\/p>\n

Show Solution<\/span><\/p>\n
855 milliliters<\/div>\n<\/div>\n

One serving of cranberry juice contains [latex]30[\/latex] grams of sugar. How many kilograms of sugar are in [latex]30[\/latex] servings of cranberry juice?<\/p>\n

One ounce of tofu provides [latex]2[\/latex] grams of protein. How many milligrams of protein are provided by [latex]5[\/latex] ounces of tofu?<\/p>\n

Show Solution<\/span><\/p>\n
10,000 milligrams<\/div>\n<\/div>\n

In the following exercises, convert between U.S. and metric units. Round to the nearest tenth.<\/strong><\/p>\n

Majid is [latex]69[\/latex] inches tall. Convert his height to centimeters.<\/p>\n

A college basketball court is [latex]84[\/latex] feet long. Convert this length to meters.<\/p>\n

Show Solution<\/span><\/p>\n
25.6 meters<\/div>\n<\/div>\n

Caroline walked [latex]2.5[\/latex] kilometers. Convert this length to miles.<\/p>\n

Lucas weighs [latex]78[\/latex] kilograms. Convert his weight to pounds.<\/p>\n

Show Solution<\/span><\/p>\n
171.6 pounds<\/div>\n<\/div>\n

Steve\u2019s car holds [latex]55[\/latex] liters of gas. Convert this to gallons.<\/p>\n

A box of books weighs [latex]25[\/latex] pounds. Convert this weight to kilograms.<\/p>\n

Show Solution<\/span><\/p>\n
11.4 kilograms<\/div>\n<\/div>\n

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.<\/strong><\/p>\n

[latex]95{^\\circ F}[\/latex]<\/p>\n

[latex]23{^\\circ F}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
\u22125\u00b0C<\/div>\n<\/div>\n

[latex]20{^\\circ F}[\/latex]<\/p>\n

[latex]64{^\\circ F}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
17.8\u00b0C<\/div>\n<\/div>\n

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.<\/strong><\/p>\n

[latex]30{^\\circ C}[\/latex]<\/p>\n

[latex]-5{^\\circ C}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
23\u00b0F<\/div>\n<\/div>\n

[latex]-12{^\\circ C}[\/latex]<\/p>\n

[latex]24{^\\circ C}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
75.2\u00b0F<\/div>\n<\/div>\n

In the following exercises, solve using the appropriate unit conversions.<\/strong><\/p>\n

Azize walked [latex]4\\Large\\frac{1}{2}[\/latex] miles. Convert this distance to feet. [latex]\\text{(1 mile}=\\text{5,280 feet).}[\/latex]<\/p>\n

One cup of milk contains [latex]276[\/latex] milligrams of calcium. Convert this to grams. [latex]\\text{(1 milligram}=\\text{0.001 gram)}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
.276 grams<\/div>\n<\/div>\n

Larry had [latex]5[\/latex] phone customer phone calls yesterday. The calls lasted [latex]28,44,9,75,\\text{and}55[\/latex] minutes. How much time, in hours and minutes, did Larry spend on the phone? [latex]\\text{(1 hour}=\\text{60 minutes)}[\/latex]<\/p>\n

Janice ran [latex]15[\/latex] kilometers. Convert this distance to miles. Round to the nearest hundredth of a mile. [latex]\\text{(1 mile}=\\text{1.61 kilometers)}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
9.317 miles<\/div>\n<\/div>\n

Yolie is [latex]63[\/latex] inches tall. Convert her height to centimeters. Round to the nearest centimeter. [latex]\\text{(1 inch}=\\text{2.54 centimeters)}[\/latex]<\/p>\n

Use the formula [latex]F=\\Large\\frac{9}{5}\\normalsize C+32[\/latex] to convert [latex]35{^\\circ C}[\/latex] to degrees [latex]\\text{F}[\/latex]<\/p>\n

Show Solution<\/span><\/p>\n
95\u00b0F<\/em><\/div>\n<\/div>\n

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