{"id":10780,"date":"2017-06-05T16:18:06","date_gmt":"2017-06-05T16:18:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10780"},"modified":"2018-01-13T19:30:04","modified_gmt":"2018-01-13T19:30:04","slug":"finding-the-volume-and-surface-area-of-a-sphere","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/finding-the-volume-and-surface-area-of-a-sphere\/","title":{"raw":"Finding the Volume and Surface Area of a Sphere","rendered":"Finding the Volume and Surface Area of a Sphere"},"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 sphere<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p data-type=\"title\">A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the center of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below.<\/p>\r\n<p data-type=\"title\">Showing where these formulas come from, like we did for a rectangular solid, is beyond the scope of this course. We will approximate [latex]\\pi [\/latex] with [latex]3.14[\/latex].<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Volume and Surface Area of a Sphere<\/h3>\r\nFor a sphere with radius [latex]r\\text{:}[\/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\/24224145\/CNX_BMath_Figure_09_06_015.png\" alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\" data-media-type=\"image\/png\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA sphere has a radius [latex]6[\/latex] inches. Find its 1. volume and 2. surface area.\r\n\r\nSolution\r\nStep 1 is the same for both 1. and 2., so we will show it just once.\r\n<table id=\"eip-id1168468504255\" class=\"unnumbered unstyled\" summary=\"The text reads, \" data-label=\"\">\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\/24224146\/CNX_BMath_Figure_09_06_042_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466046693\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 sphere<\/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 [latex]V[\/latex] = volume<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.<\/td>\r\n<td>[latex]V=\\Large\\frac{4}{3}\\normalsize\\pi {r}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]V\\approx\r\n\r\n\\Large\\frac{4}{3}\\normalsize\\left(3.14\\right){6}^{3}[\/latex]\r\n\r\n[latex]V\\approx 904.32\\text{cubic inches}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> Double-check your math on a calculator.<\/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]904.32[\/latex] cubic inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467263246\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 cube<\/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 data-effect=\"italics\">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.<\/td>\r\n<td>[latex]S=4\\pi {r}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]S\\approx 4\\left(3.14\\right){6}^{2}[\/latex]\r\n\r\n[latex]S\\approx 452.16[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> Double-check your math on a calculator<\/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]452.16[\/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]146804[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA globe of Earth is in the shape of a sphere with radius [latex]14[\/latex] centimeters. Find its 1. volume and 2. surface area. Round the answer to the nearest hundredth.\r\n[reveal-answer q=\"508164\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"508164\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467368787\" class=\"unnumbered unstyled\" summary=\"Step 1. Read the problem.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw a figure with the\r\n\r\ngiven information and label it.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224147\/CNX_BMath_Figure_09_06_043_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168464926516\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 sphere<\/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 [latex]V[\/latex] = 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 3.14 for [latex]\\pi [\/latex] )<\/td>\r\n<td>[latex]V=\\Large\\frac{4}{3}\\normalsize\\pi {r}^{3}[\/latex]\r\n\r\n[latex]V\\approx \\Large\\frac{4}{3}\\normalsize\\left(3.14\\right){14}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]V\\approx 11,488.21[\/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]11,488.21[\/latex] cubic inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468466725\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 sphere<\/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 data-effect=\"italics\">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 3.14 for [latex]\\pi [\/latex] )<\/td>\r\n<td>[latex]S=4\\pi {r}^{2}[\/latex]\r\n\r\n[latex]S\\approx 4\\left(3.14\\right){14}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve.<\/strong><\/td>\r\n<td>[latex]S\\approx 2461.76[\/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]2461.76[\/latex] square inches.<\/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]146806[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show an example of how to find the surface area of a sphere.\r\n\r\nhttps:\/\/youtu.be\/OLlEbk1xGm4\r\n\r\nAnd in our final video we show an example of how to find the volume of a sphere given it's diameter.\r\n\r\nhttps:\/\/youtu.be\/_kejcXbRjGY","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the volume and surface area of a sphere<\/li>\n<\/ul>\n<\/div>\n<p data-type=\"title\">A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the center of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below.<\/p>\n<p data-type=\"title\">Showing where these formulas come from, like we did for a rectangular solid, is beyond the scope of this course. We will approximate [latex]\\pi[\/latex] with [latex]3.14[\/latex].<\/p>\n<div class=\"textbox shaded\">\n<h3>Volume and Surface Area of a Sphere<\/h3>\n<p>For a sphere with radius [latex]r\\text{:}[\/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\/24224145\/CNX_BMath_Figure_09_06_015.png\" alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\" data-media-type=\"image\/png\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A sphere has a radius [latex]6[\/latex] inches. Find its 1. volume and 2. surface area.<\/p>\n<p>Solution<br \/>\nStep 1 is the same for both 1. and 2., so we will show it just once.<\/p>\n<table id=\"eip-id1168468504255\" class=\"unnumbered unstyled\" summary=\"The text reads,\" data-label=\"\">\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\/24224146\/CNX_BMath_Figure_09_06_042_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466046693\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let [latex]V[\/latex] = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/td>\n<td>[latex]V=\\Large\\frac{4}{3}\\normalsize\\pi {r}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]V\\approx    \\Large\\frac{4}{3}\\normalsize\\left(3.14\\right){6}^{3}[\/latex]<\/p>\n<p>[latex]V\\approx 904.32\\text{cubic inches}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> Double-check your math on a calculator.<\/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]904.32[\/latex] cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467263246\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/td>\n<td>[latex]S=4\\pi {r}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]S\\approx 4\\left(3.14\\right){6}^{2}[\/latex]<\/p>\n<p>[latex]S\\approx 452.16[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> Double-check your math on a calculator<\/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]452.16[\/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=\"ohm146804\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146804&theme=oea&iframe_resize_id=ohm146804&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>A globe of Earth is in the shape of a sphere with radius [latex]14[\/latex] centimeters. Find its 1. volume and 2. surface area. Round the answer to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q508164\">Show Solution<\/span><\/p>\n<div id=\"q508164\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467368787\" class=\"unnumbered unstyled\" summary=\"Step 1. Read the problem.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw a figure with the<\/p>\n<p>given information and label it.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224147\/CNX_BMath_Figure_09_06_043_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168464926516\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let [latex]V[\/latex] = 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 3.14 for [latex]\\pi[\/latex] )<\/td>\n<td>[latex]V=\\Large\\frac{4}{3}\\normalsize\\pi {r}^{3}[\/latex]<\/p>\n<p>[latex]V\\approx \\Large\\frac{4}{3}\\normalsize\\left(3.14\\right){14}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]V\\approx 11,488.21[\/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]11,488.21[\/latex] cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468466725\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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 sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">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 3.14 for [latex]\\pi[\/latex] )<\/td>\n<td>[latex]S=4\\pi {r}^{2}[\/latex]<\/p>\n<p>[latex]S\\approx 4\\left(3.14\\right){14}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve.<\/strong><\/td>\n<td>[latex]S\\approx 2461.76[\/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]2461.76[\/latex] square inches.<\/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=\"ohm146806\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146806&theme=oea&iframe_resize_id=ohm146806&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show an example of how to find the surface area of a sphere.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Find the Surface Area of a Sphere\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/OLlEbk1xGm4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>And in our final video we show an example of how to find the volume of a sphere given it&#8217;s diameter.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Volume of a Sphere\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/_kejcXbRjGY?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-10780\">\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 146804, 146806. <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>Find the Surface Area of a Sphere. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/OLlEbk1xGm4\">https:\/\/youtu.be\/OLlEbk1xGm4<\/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>Ex: Volume of a Sphere. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/_kejcXbRjGY\">https:\/\/youtu.be\/_kejcXbRjGY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/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":17533,"menu_order":19,"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 146804, 146806\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Find the Surface Area of a Sphere\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/OLlEbk1xGm4\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Volume of a Sphere\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/_kejcXbRjGY\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"6e29be64-008a-45ca-a3f1-eb9ff28a96b2","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10780","chapter","type-chapter","status-publish","hentry"],"part":7831,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10780","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":16,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10780\/revisions"}],"predecessor-version":[{"id":15680,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10780\/revisions\/15680"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/7831"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10780\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=10780"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=10780"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=10780"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=10780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}