Module 6 Problems

  1. Find the supplement and the complement of a [latex]{53^\circ }[/latex] angle.
  2. Find the supplement and the complement of a [latex]{16^\circ }[/latex] angle.
  3. Find the supplement and the complement of a [latex]{29^\circ }[/latex] angle.
  4. Find the supplement and the complement of a [latex]{72^\circ }[/latex] angle.
  5. Find the supplement of a [latex]{135^\circ }[/latex] angle.
  6. Find the complement of a [latex]{38^\circ }[/latex] angle.
  7. Find the complement of a [latex]27.5^\circ[/latex] angle.
  8. Find the supplement of a [latex]109.5^\circ[/latex] angle.
  9. Two angles are supplementary. The larger angle is [latex]{56^\circ }[/latex] more than the smaller angle. Find the measures of both angles.
  10. Two angles are supplementary. The smaller angle is [latex]{36^\circ }[/latex] less than the larger angle. Find the measures of both angles.
  11. Two angles are complementary. The smaller angle is [latex]{34^\circ }[/latex] less than the larger angle. Find the measures of both angles.
  12. Two angles are complementary. The larger angle is [latex]{52^\circ }[/latex] more than the smaller angle. Find the measures of both angles.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. One angle of a right triangle measures [latex]{33^\circ }[/latex]. What is the measure of the other angle?
  18. One angle of a right triangle measures [latex]{51^\circ }[/latex]. What is the measure of the other angle?
  19. One angle of a right triangle measures [latex]22.5^\circ[/latex]. What is the measure of the other angle?
  20. One angle of a right triangle measures [latex]36.5^\circ[/latex]. What is the measure of the other angle?
  21. The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.
  22. 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.
  23. Would you measure the amount of sand in a sandbag using linear, square or cubic measure?
  24. Would you measure the height of a tree using linear, square or cubic measure?
  25. Would you measure the size of a patio using linear, square or cubic measure?
  26. Would you measure the length of a highway using linear, square or cubic measure?
  27. The length of a rectangle is [latex]42[/latex] meters and the width is [latex]28[/latex] meters.  Find the perimeter and area.
  28. The length of a rectangle is [latex]36[/latex] feet and the width is [latex]19[/latex] feet. Find the perimeter and area.
  29. A sidewalk in front of Kathy’s house is in the shape of a rectangle [latex]4[/latex] feet wide by [latex]45[/latex] feet long.  Find the perimeter and are of the sidewalk.
  30. A rectangular room is [latex]16[/latex] feet wide by [latex]12[/latex] feet long.  Find the perimeter and area of the room.
  31. Find the length of a rectangle with perimeter of [latex]220[/latex] centimeters and width of [latex]85[/latex] centimeters.
  32. Find the width of a rectangle with perimeter [latex]39[/latex] and length [latex]11[/latex].
  33. The area of a rectangle is [latex]2356[/latex] square meters. The length is [latex]38[/latex] meters. What is the width?
  34. The width of a rectangle is [latex]45[/latex] centimeters. The area is [latex]2700[/latex] square centimeters. What is the length?
  35. 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.
  36. 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.
  37. Find the area of a triangle with base [latex]18[/latex] inches and height [latex]15[/latex] inches.
  38. Find the area of a triangle with base [latex]33[/latex] centimeters and height [latex]21[/latex] centimeters.
  39. A triangular road sign has base [latex]30[/latex] inches and height [latex]40[/latex] inches. What is its area?
  40. 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?
  41. 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.
  42. Find the length of each side of an equilateral triangle with perimeter of [latex]81[/latex] yards.
  43. 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?
  44. 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?
  45. Find the area of the trapezoid with height [latex]25[/latex] meters and bases [latex]32.5[/latex] and [latex]21.5[/latex] meters.
  46. 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?
  47. Jose just removed the children’s 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?
  48. 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.
  49. 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?
  50. A circular mosaic has radius [latex]3[/latex] meters. Find the ⓐ circumference ⓑ area of the mosaic.  Round your answers to the nearest hundredth.
  51. A circular fountain has radius [latex]8[/latex] feet. Find the ⓐ circumference ⓑ area of the fountain. Round your answers to the nearest hundredth.
  52. Find the diameter of a circle with circumference [latex]150.72[/latex] inches.
  53. Find the radius of a circle with circumference [latex]345.4[/latex] centimeters.
  54. Find the area of the shaded region.
  55. Find the area of the shaded region.  A geometric shape is shown. It is a U-shape. The base is labeled 5, the height 6. The horizontal and vertical lines at the top are labeled 2.  A geometric shape is shown, formed by two rectangles. The top is labeled 8. The width of the top rectangle is labeled 3. The right side of the figure is labeled 5. The width of the bottom rectangle is labeled 3.
  56. Find the area of the shaded region.  A geometric shape is shown. It is formed by two triangles. The shared base of the two triangles is labeled 20. The height of each triangle is labeled 15.
  57. Find the area of the shaded region.  A geometric shape is shown. It is a trapezoid with a triangle attached to the top on the right side. The height of the trapezoid is labeled 8, the bottom base is labeled 12, and the top is labeled 9. The height of the triangle is labeled 8.
  58. Find the area of the shaded region.A geometric shape is shown. It is a rectangle with a semi-circle attached to the top. The base of the rectangle, also the diameter of the semi-circle, is labeled 10. The height of the rectangle is labeled 16.
  59. Find the volume and surface area of a rectangular solid with length [latex]14[/latex] centimeters, width [latex]4.5[/latex] centimeters, and height [latex]10[/latex] centimeters.
  60. Find the volume and surface area of a cube with sides that are [latex]3[/latex] feet long.
  61. Find the volume and surface area of a cube of tofu with sides [latex]2.5[/latex] inches.
  62. Find the volume and surface area of a rectangular carton with length [latex]32[/latex] inches, width [latex]18[/latex] inches, and height [latex]10[/latex] inches
  63. Find the volume and surface area of a sphere with radius [latex]4[/latex] yards.
  64. Find the volume and surface area of a sphere with radius [latex]12[/latex] meters.
  65. Find the volume and surface area of a baseball with radius [latex]1.45[/latex] inches.
  66. Find the volume and surface area of a soccer ball with radius [latex]22[/latex] centimeters.
  67. Find the volume and surface area of a cylinder with radius [latex]2[/latex] yards and height [latex]6[/latex] yards.
  68. Find the volume and surface area of a cylinder with diameter [latex]18[/latex] inches and height [latex]40[/latex] inches.
  69. Find the volume and surface area of a juice can with diameter [latex]8[/latex] centimeters and height [latex]15[/latex] centimeters.
  70. Find the volume and surface area of a cylindrical pylon with diameter [latex]0.8[/latex] feet and height [latex]2.5[/latex] feet.
  71. Find the volume of a cone with height [latex]5[/latex] meters and radius [latex]1[/latex] meter.
  72. Find the volume of a cone with height [latex]24[/latex] feet and radius [latex]8[/latex] feet.
  73. Find the volume of a cone-shaped water cup with diameter [latex]2.6[/latex] inches and height [latex]2.6[/latex] inches.
  74. Find the volume of a cone-shaped pile of gravel with diameter [latex]6[/latex] yards and height [latex]5[/latex] yards.
  75. A rectangular moving van has length [latex]16[/latex] feet, width [latex]8[/latex] feet, and height [latex]8[/latex] feet. How much can it hold?
  76. A rectangular gift box has length [latex]26[/latex] inches, width [latex]16[/latex] inches, and height [latex]4[/latex] inches. How much can it hold?
  77. The base of a statue is a cube with sides [latex]2.8[/latex] meters long. Find its volume and surface area.
  78. A box of tissues is a cube with sides 4.5 inches long. Find its volume and surface area.
  79. An exercise ball has a radius of [latex]15[/latex] inches. Find its volume and surface area.
  80. A golf ball has a radius of [latex]4.5[/latex] centimeters. Find its volume and surface area.
  81. A can of coffee has a radius of [latex]5[/latex] cm and a height of [latex]13[/latex] cm. Find its volume and surface area.
  82. A cylindrical column has a diameter of [latex]8[/latex] feet and a height of [latex]28[/latex] feet. Find its volume and surface area.
  83. 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?
  84. 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?
  85. 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, ⓐ find the volume of the regular ice cream cone. ⓑ find the volume of the waffle cone. ⓒ how much more ice cream fits in the waffle cone compared to the regular cone?