{"id":4460,"date":"2020-04-13T13:45:24","date_gmt":"2020-04-13T13:45:24","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4460"},"modified":"2020-04-13T13:45:24","modified_gmt":"2020-04-13T13:45:24","slug":"finding-the-volume-and-surface-area-of-a-cylinder","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/finding-the-volume-and-surface-area-of-a-cylinder\/","title":{"raw":"Finding the Volume and Surface Area of a Cylinder","rendered":"Finding the Volume and Surface Area of a Cylinder"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find the volume and surface area of a cylinder<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>If you have ever seen a can of soda, you know what a cylinder looks like. A cylinder is a solid figure with two parallel circles of the same size at the top and bottom. The top and bottom of a cylinder are called the bases. The height [latex]h[\/latex] of a cylinder is the distance between the two bases. For all the cylinders we will work with here, the sides and the height, [latex]h[\/latex] , will be perpendicular to the bases.<\/p>\r\nA cylinder has two circular bases of equal size. The height is the distance between the bases.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224148\/CNX_BMath_Figure_09_06_020_img.png\" alt=\"An image of a cylinder is shown. There is a red arrow pointing to the radius of the top labeling it r, radius. There is a red arrow pointing to the height of the cylinder labeling it h, height.\" \/>\r\nRectangular solids and cylinders are somewhat similar because they both have two bases and a height. The formula for the volume of a rectangular solid, [latex]V=Bh[\/latex] , can also be used to find the volume of a cylinder.\r\n\r\nFor the rectangular solid, the area of the base, [latex]B[\/latex] , is the area of the rectangular base, length \u00d7 width. For a cylinder, the area of the base, [latex]B[\/latex], is the area of its circular base, [latex]\\pi {r}^{2}[\/latex]. The image below compares how the formula [latex]V=Bh[\/latex] is used for rectangular solids and cylinders.\r\n\r\nSeeing how a cylinder is similar to a rectangular solid may make it easier to understand the formula for the volume of a cylinder.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224149\/CNX_BMath_Figure_09_06_021.png\" alt=\"In (a), a rectangular solid is shown. The sides are labeled L, W, and H. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses lw times h, then V equals lwh. In (b), a cylinder is shown. The radius of the top is labeled r, the height is labeled h. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses pi r squared times h, then V equals pi times r squared times h.\" \/>\r\nTo understand the formula for the surface area of a cylinder, think of a can of vegetables. It has three surfaces: the top, the bottom, and the piece that forms the sides of the can. If you carefully cut the label off the side of the can and unroll it, you will see that it is a rectangle. See the image below.\r\n\r\nBy cutting and unrolling the label of a can of vegetables, we can see that the surface of a cylinder is a rectangle. The length of the rectangle is the circumference of the cylinder\u2019s base, and the width is the height of the cylinder.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224151\/CNX_BMath_Figure_09_06_022.png\" alt=\"A cylindrical can of green beans is shown. The height is labeled h. Beside this are pictures of circles for the top and bottom of the can and a rectangle for the other portion of the can. Above the circles is C equals 2 times pi times r. The top of the rectangle says l equals 2 times pi times r. The left side of the rectangle is labeled h, the right side is labeled w.\" \/>\r\nThe distance around the edge of the can is the circumference of the cylinder\u2019s base it is also the length [latex]L[\/latex] of the rectangular label. The height of the cylinder is the width [latex]W[\/latex] of the rectangular label. So the area of the label can be represented as\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224152\/CNX_BMath_Figure_09_06_023_img.png\" alt=\"The top line says A equals l times red w. Below the l is 2 times pi times r. Below the w is a red h.\" \/>\r\nTo find the total surface area of the cylinder, we add the areas of the two circles to the area of the rectangle.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224153\/CNX_BMath_Figure_09_06_044_img.png\" alt=\"A rectangle is shown with circles coming off the top and bottom.\" \/>\r\nThe surface area of a cylinder with radius [latex]r[\/latex] and height [latex]h[\/latex], is\r\n\r\n[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]\r\n<div class=\"textbox shaded\">\r\n<h3>Volume and Surface Area of a Cylinder<\/h3>\r\nFor a cylinder with radius [latex]r[\/latex] and height [latex]h:[\/latex]\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224155\/CNX_BMath_Figure_09_06_024.png\" alt=\"A cylinder is shown. The height is labeled h and the radius of the top is labeled r. Beside it is Volume: V equals pi times r squared times h or V equals capital B times h. Below this is Surface Area: S equals 2 times pi times r squared plus 2 times pi times r times h.\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA cylinder has height [latex]5[\/latex] centimeters and radius [latex]3[\/latex] centimeters. Find the 1. volume and 2. surface area.\r\n\r\nSolution\r\n<table id=\"fs-id1168466110662\" class=\"unnumbered unstyled\" summary=\"The text reads, \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label\r\n\r\nit with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224156\/CNX_BMath_Figure_09_06_046_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469800646\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the volume of the cylinder<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em>V<\/em> = volume<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.\r\n\r\nSubstitute. (Use [latex]3.14[\/latex] for [latex]\\pi [\/latex] )<\/td>\r\n<td>[latex]V=\\pi {r}^{2}h[\/latex]\r\n\r\n[latex]V\\approx \\left(3.14\\right){3}^{2}\\cdot 5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]V\\approx 141.3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check your calculations.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The volume is approximately [latex]141.3[\/latex] cubic inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468464551\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the surface area of the cylinder<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em>S<\/em> = surface area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.\r\n\r\nSubstitute. (Use [latex]3.14[\/latex] for [latex]\\pi [\/latex] )<\/td>\r\n<td>[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]\r\n\r\n[latex]S\\approx 2\\left(3.14\\right){3}^{2}+2\\left(3.14\\right)\\left(3\\right)5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]S\\approx 150.72[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check your calculations.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The surface area is approximately [latex]150.72[\/latex] square inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146810[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the 1. volume and 2. surface area of a can of soda. The radius of the base is [latex]4[\/latex] centimeters and the height is [latex]13[\/latex] centimeters. Assume the can is shaped exactly like a cylinder.\r\n\r\n[reveal-answer q=\"577687\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"577687\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468414539\" class=\"unnumbered unstyled\" summary=\"The text reads, \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and\r\n\r\nlabel it with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224157\/CNX_BMath_Figure_09_06_047_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468670924\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the volume of the cylinder<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em>V<\/em> = volume<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.\r\n\r\nSubstitute. (Use [latex]3.14[\/latex] for [latex]\\pi [\/latex] )<\/td>\r\n<td>[latex]V=\\pi {r}^{2}h[\/latex]\r\n\r\n[latex]V\\approx \\left(3.14\\right){4}^{2}\\cdot 13[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]V\\approx 653.12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The volume is approximately [latex]653.12[\/latex] cubic centimeters.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467199006\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the surface area of the cylinder<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em>S<\/em> = surface area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.\r\n\r\nSubstitute. (Use [latex]3.14[\/latex] for [latex]\\pi [\/latex] )<\/td>\r\n<td>[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]\r\n\r\n[latex]S\\approx 2\\left(3.14\\right){4}^{2}+2\\left(3.14\\right)\\left(4\\right)13[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]S\\approx 427.04[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check your calculations.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The surface area is approximately [latex]427.04[\/latex] square centimeters.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146815[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video shows an example of ho to find the volume of a cylinder.\r\n\r\nhttps:\/\/youtu.be\/oDgfx-Kztrk\r\n\r\nIn the next example video we show how to find the surface area of a cylinder.\r\n\r\nhttps:\/\/youtu.be\/CN_7ZxmixXY","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the volume and surface area of a cylinder<\/li>\n<\/ul>\n<\/div>\n<p>If you have ever seen a can of soda, you know what a cylinder looks like. A cylinder is a solid figure with two parallel circles of the same size at the top and bottom. The top and bottom of a cylinder are called the bases. The height [latex]h[\/latex] of a cylinder is the distance between the two bases. For all the cylinders we will work with here, the sides and the height, [latex]h[\/latex] , will be perpendicular to the bases.<\/p>\n<p>A cylinder has two circular bases of equal size. The height is the distance between the bases.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224148\/CNX_BMath_Figure_09_06_020_img.png\" alt=\"An image of a cylinder is shown. There is a red arrow pointing to the radius of the top labeling it r, radius. There is a red arrow pointing to the height of the cylinder labeling it h, height.\" \/><br \/>\nRectangular solids and cylinders are somewhat similar because they both have two bases and a height. The formula for the volume of a rectangular solid, [latex]V=Bh[\/latex] , can also be used to find the volume of a cylinder.<\/p>\n<p>For the rectangular solid, the area of the base, [latex]B[\/latex] , is the area of the rectangular base, length \u00d7 width. For a cylinder, the area of the base, [latex]B[\/latex], is the area of its circular base, [latex]\\pi {r}^{2}[\/latex]. The image below compares how the formula [latex]V=Bh[\/latex] is used for rectangular solids and cylinders.<\/p>\n<p>Seeing how a cylinder is similar to a rectangular solid may make it easier to understand the formula for the volume of a cylinder.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224149\/CNX_BMath_Figure_09_06_021.png\" alt=\"In (a), a rectangular solid is shown. The sides are labeled L, W, and H. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses lw times h, then V equals lwh. In (b), a cylinder is shown. The radius of the top is labeled r, the height is labeled h. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses pi r squared times h, then V equals pi times r squared times h.\" \/><br \/>\nTo understand the formula for the surface area of a cylinder, think of a can of vegetables. It has three surfaces: the top, the bottom, and the piece that forms the sides of the can. If you carefully cut the label off the side of the can and unroll it, you will see that it is a rectangle. See the image below.<\/p>\n<p>By cutting and unrolling the label of a can of vegetables, we can see that the surface of a cylinder is a rectangle. The length of the rectangle is the circumference of the cylinder\u2019s base, and the width is the height of the cylinder.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224151\/CNX_BMath_Figure_09_06_022.png\" alt=\"A cylindrical can of green beans is shown. The height is labeled h. Beside this are pictures of circles for the top and bottom of the can and a rectangle for the other portion of the can. Above the circles is C equals 2 times pi times r. The top of the rectangle says l equals 2 times pi times r. The left side of the rectangle is labeled h, the right side is labeled w.\" \/><br \/>\nThe distance around the edge of the can is the circumference of the cylinder\u2019s base it is also the length [latex]L[\/latex] of the rectangular label. The height of the cylinder is the width [latex]W[\/latex] of the rectangular label. So the area of the label can be represented as<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224152\/CNX_BMath_Figure_09_06_023_img.png\" alt=\"The top line says A equals l times red w. Below the l is 2 times pi times r. Below the w is a red h.\" \/><br \/>\nTo find the total surface area of the cylinder, we add the areas of the two circles to the area of the rectangle.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224153\/CNX_BMath_Figure_09_06_044_img.png\" alt=\"A rectangle is shown with circles coming off the top and bottom.\" \/><br \/>\nThe surface area of a cylinder with radius [latex]r[\/latex] and height [latex]h[\/latex], is<\/p>\n<p>[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]<\/p>\n<div class=\"textbox shaded\">\n<h3>Volume and Surface Area of a Cylinder<\/h3>\n<p>For a cylinder with radius [latex]r[\/latex] and height [latex]h:[\/latex]<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224155\/CNX_BMath_Figure_09_06_024.png\" alt=\"A cylinder is shown. The height is labeled h and the radius of the top is labeled r. Beside it is Volume: V equals pi times r squared times h or V equals capital B times h. Below this is Surface Area: S equals 2 times pi times r squared plus 2 times pi times r times h.\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A cylinder has height [latex]5[\/latex] centimeters and radius [latex]3[\/latex] centimeters. Find the 1. volume and 2. surface area.<\/p>\n<p>Solution<\/p>\n<table id=\"fs-id1168466110662\" class=\"unnumbered unstyled\" summary=\"The text reads,\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label<\/p>\n<p>it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224156\/CNX_BMath_Figure_09_06_046_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469800646\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em>V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/p>\n<p>Substitute. (Use [latex]3.14[\/latex] for [latex]\\pi[\/latex] )<\/td>\n<td>[latex]V=\\pi {r}^{2}h[\/latex]<\/p>\n<p>[latex]V\\approx \\left(3.14\\right){3}^{2}\\cdot 5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]V\\approx 141.3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The volume is approximately [latex]141.3[\/latex] cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468464551\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em>S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/p>\n<p>Substitute. (Use [latex]3.14[\/latex] for [latex]\\pi[\/latex] )<\/td>\n<td>[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]<\/p>\n<p>[latex]S\\approx 2\\left(3.14\\right){3}^{2}+2\\left(3.14\\right)\\left(3\\right)5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]S\\approx 150.72[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately [latex]150.72[\/latex] square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146810\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146810&theme=oea&iframe_resize_id=ohm146810&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the 1. volume and 2. surface area of a can of soda. The radius of the base is [latex]4[\/latex] centimeters and the height is [latex]13[\/latex] centimeters. Assume the can is shaped exactly like a cylinder.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q577687\">Show Solution<\/span><\/p>\n<div id=\"q577687\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468414539\" class=\"unnumbered unstyled\" summary=\"The text reads,\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and<\/p>\n<p>label it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224157\/CNX_BMath_Figure_09_06_047_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468670924\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em>V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/p>\n<p>Substitute. (Use [latex]3.14[\/latex] for [latex]\\pi[\/latex] )<\/td>\n<td>[latex]V=\\pi {r}^{2}h[\/latex]<\/p>\n<p>[latex]V\\approx \\left(3.14\\right){4}^{2}\\cdot 13[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]V\\approx 653.12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The volume is approximately [latex]653.12[\/latex] cubic centimeters.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467199006\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em>S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/p>\n<p>Substitute. (Use [latex]3.14[\/latex] for [latex]\\pi[\/latex] )<\/td>\n<td>[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]<\/p>\n<p>[latex]S\\approx 2\\left(3.14\\right){4}^{2}+2\\left(3.14\\right)\\left(4\\right)13[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]S\\approx 427.04[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately [latex]427.04[\/latex] square centimeters.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146815\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146815&theme=oea&iframe_resize_id=ohm146815&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video shows an example of ho to find the volume of a cylinder.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Volume of a Cylinder\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/oDgfx-Kztrk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next example video we show how to find the surface area of a cylinder.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Find the surface Area of a Cylinder\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/CN_7ZxmixXY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4460\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146815, 146810. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Volume of a Cylinder. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/oDgfx-Kztrk\">https:\/\/youtu.be\/oDgfx-Kztrk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Find the Surface Area of a Cylinder. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/CN_7ZxmixXY\">https:\/\/youtu.be\/CN_7ZxmixXY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146815, 146810\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Volume of a Cylinder\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/oDgfx-Kztrk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Find the Surface Area of a Cylinder\",\"author\":\"James Sousa 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