{"id":4552,"date":"2013-06-29T06:45:11","date_gmt":"2013-06-29T06:45:11","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4552"},"modified":"2026-03-26T09:38:48","modified_gmt":"2026-03-26T14:38:48","slug":"volume-and-surface-area-of-a-cube","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/volume-and-surface-area-of-a-cube\/","title":{"rendered":"Volume and Surface Area of a Cube"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_nU6oAvMa_ZM\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_nU6oAvMa_ZM\" data-source-videoID=\"nU6oAvMa_ZM\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Volume and Surface Area of a Cube Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Volume and Surface Area of a Cube\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_nU6oAvMa_ZM:hover {cursor:pointer;} img#videoThumbnailImage_nU6oAvMa_ZM {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/746-volume-and-surface-area-of-a-cube-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_nU6oAvMa_ZM\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_nU6oAvMa_ZM\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Volume and Surface Area of a Cube\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_nU6oAvMa_ZM\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_nU6oAvMa_ZM\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_nU6oAvMa_ZM\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction YuA_Function() {\n  var x = document.getElementById(\"YuA\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"YuA_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"YuA\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Volume_of_a_Cube\" class=\"smooth-scroll\">Volume of a Cube<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Surface_Area_of_a_Cube\" class=\"smooth-scroll\">Surface Area of a Cube<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Volume_and_Surface_Area_of_a_Cube_Practice_Questions\" class=\"smooth-scroll\">Volume and Surface Area of a Cube Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video about the volume and surface area of a cube!<\/p>\n<p>We see this shape everywhere, most commonly with blocks and dice. And then there\u2019s the colorful puzzle known as a Rubik\u2019s Cube, which is a cube that appears to be made up of smaller cubes. <\/p>\n<p>In math, a cube is a special kind of rectangular prism. In most rectangular prisms, the length, width, and height of the shape can all be different. But in a cube, they\u2019re all the same. That is to say that the edges are all the same length. <\/p>\n<h2><span id=\"Volume_of_a_Cube\" class=\"m-toc-anchor\"><\/span>Volume of a Cube<\/h2>\n<p>\nThere are two important measures of a cube. The first one is the volume. The volume of a cube or any other 3D object is a measure of how much space it takes up. We measure this in cubic units such as cubic inches or cubic centimeters. It\u2019s easy to picture this with a cube. Just imagine that we have a bunch of little cubes that are one centimeter tall, one centimeter wide, and one centimeter long. Each one of these cubes is one cubic centimeter. This is our unit of measure. <\/p>\n<p>Now let\u2019s build something from these little cubes. Let\u2019s build something that looks a lot like a Rubik\u2019s Cube. We\u2019ll start with the top level. We need to make a three-by-three grid of the cubes. Each cube is one centimeter tall and one centimeter wide. Once we\u2019re done with that layer we can see that we\u2019ve used nine cubes. Next, we build the middle level using another nine cubes. All together, 9 and 9 make 18 cubic centimeters. Finally, we build the bottom level, again using nine more cubes. All together we\u2019ve got 27 cubic centimeters.<\/p>\n<p>Our finished shape is a cube made up of smaller cubes. How many did we use? Nine on each layer for a total of 27. We used 27 one-centimeter cubes (or cubic centimeters) to make our bigger cube. <\/p>\n<h3><span id=\"Volume_of_a_Cube_Formula\" class=\"m-toc-anchor\"><\/span>Volume of a Cube Formula<\/h3>\n<p>\nFortunately, to find the volume of every cube we don\u2019t need to build one out of smaller cubes\u2014there is a formula we can use instead. The formula for the volume of a cube is \\(V = a^3\\). \\(V\\) is the volume and \\(a\\) is the length of an edge (remember that all the edges have the same length).<\/p>\n<p>If we measure the area of this cube, we find that all the edges are 3 centimeters long. So to find the volume we can substitute 3 for \\(a\\) in our formula. We raise it to the third power \\((3\\times 3\\times 3)\\) which gets us \\(27\\text{ cm}^3\\), which makes sense since we needed to use 27 of the little cubes to build our cube. Remember that it\u2019s very important to specify the units when giving our answer. <\/p>\n<h2><span id=\"Surface_Area_of_a_Cube\" class=\"m-toc-anchor\"><\/span>Surface Area of a Cube<\/h2>\n<p>\nThe other main measure of a cube is surface area. It\u2019s an area measurement, so it\u2019s in two dimensions. Imagine we were making a paper case for the cube we built earlier. How much paper would we need, in square centimeters? If we look at the cube we built earlier and just look at one side of it, we can see a bunch of these one-centimeter squares. If we count them we can see there are nine, in fact. So one side is made of nine square centimeters. <\/p>\n<p>But to find the surface area of the cube we need the area of all the sides, not just one. Fortunately, since a cube is the same length, width and height that means that all the sides have the same area. And there are six sides. So we can multiply 6 sides by the area of one side (in this case, \\(9\\text{ cm}^2\\)) to find a total surface area of \\(54\\text{ cm}^2\\). That\u2019s how much paper we\u2019d need to make our paper case. <\/p>\n<h3><span id=\"Surface_Area_of_a_Cube_Formula\" class=\"m-toc-anchor\"><\/span>Surface Area of a Cube Formula<\/h3>\n<p>\nYou may have seen a \u201cmap\u201d like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/17.png\" alt=\"A cube has been unfolded into six squares, the leftmost of which is a 3x3 grid\" width=\"680\" height=\"386\" class=\"aligncenter size-full wp-image-108039\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/17.png 680w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/17-300x170.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Just like with <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/how-to-find-the-volume-of-3d-objects\/\">volume<\/a>, we have a formula so we don\u2019t have to build a cube each time we need to find the surface area. The formula is \\(\\text{Surface Area} = 6a^2\\). The 6 represents the number of sides of the cube, and the \\(a^2\\) is the area for each side. We can confirm that this works by plugging in our edge length, \\(6(3)^2\\), and then evaluating the expression. <\/p>\n<p>We need to remember to use the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/order-of-operations\/\">order of operations<\/a> and apply the exponent before we multiply. If we do so, we see that we correctly figure out the surface area of \\(54\\text{ cm}^2\\) for our cube. <\/p>\n<p>Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Volume_and_Surface_Area_of_a_Cube_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Volume and Surface Area of a Cube Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the surface area of this cube?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Cube-Volume-and-Surface-Area-Example-1.svg\" alt=\"A wireframe cube with each side labeled as 4 inches.\" width=\"299.2\" height=\"236.3\" class=\"aligncenter size-full wp-image-287321\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">16 in<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-2\">64 in<sup>2<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">96 in<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-4\">112 in<sup>2<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for surface area of a cube is \\(SA=6s^2\\). Plug in 4 in for \\(s\\) and solve.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\\(SA=6s^2=6(4)^2=6(16)\\)\\(\\:=96\\text{ in}^2\\)<\/p>\n<p>Therefore, the surface area of the cube is 96 in<sup>2<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the volume of this cube?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Cube-Volume-and-Surface-Area-Example-2.svg\" alt=\"A wireframe diagram of a cube with each side labeled as 3 feet.\" width=\"254.15\" height=\"259.25\" class=\"aligncenter size-full wp-image-287324\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">27 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-2\">36 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-3\">54 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-4\">81 ft<sup>3<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for volume of a cube is \\(V=s^3\\). Plug in 3 feet for \\(s\\) and solve.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\\(V=s^3=(3\\text{ ft})^3=27\\text{ ft}^3\\)<\/p>\n<p>Therefore, the volume of the cube is 27 ft<sup>3<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the surface area of a cube with side length of 12 meters?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">1,728 m<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-3-2\">1,120 m<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-3-3\">144 m<sup>2<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">864 m<sup>2<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for surface area of a cube is \\(SA=6s^2\\). Plug in 12 meters for \\(s\\) and solve. <\/p>\n<p style=\"text-align:center; line-height: 35px\">\\(SA=6s^2=6(12\\text{ m})^2=6(144\\text{ m}^2)\\)\\(\\:=864\\text{ m}^2\\)<\/p>\n<p>Therefore, the surface area of the cube is 864 m<sup>2<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the volume of a cube with a surface area of 96 m<sup>2<\/sup>?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">96 m<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\">64 m<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-4-3\">16 m<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-4-4\">864 m<sup>2<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the volume of a cube given the surface area, first use the surface area formula to find the side length, then use the side length to find the volume.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\(6s^2=96\\text{ m}^2\\)<br \/>\n\\(s^2=16\\text{ m}^2\\)<br \/>\n\\(s=4\\text{ m}\\)\n<\/p>\n<p>The side length of this cube is 4 meters. Now, plug this value into the volume formula and solve.<\/p>\n<p style=\"text-align:center;\">\\(V=s^3=(4\\text{ m})^3=64\\text{ m}^3\\)<\/p>\n<p>Therefore, the volume of this cube is 64 m<sup>3<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nIf units are ignored, what is the difference between the volume and surface area of a cube with side length 7?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">49<\/div><div class=\"PQ\"  id=\"PQ-5-2\">23<\/div><div class=\"PQ\"  id=\"PQ-5-3\">17<\/div><div class=\"PQ\"  id=\"PQ-5-4\">64<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To solve this problem, we need to plug 7 in for \\(s\\) and solve for both volume and surface area, and then subtract the two values.<\/p>\n<p>First, find the volume of the cube.<\/p>\n<p style=\"text-align:center;\">\\(V=s^3=(7)^3=343\\)<\/p>\n<p>Then, find the surface area of the cube.<\/p>\n<p style=\"text-align:center;\">\\(SA=6s^2=6(7)^2=6(49)=294\\)<\/p>\n<p>Finally, subtract the surface area from the volume.<\/p>\n<p style=\"text-align:center;\">\\(343-294=49\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":99838,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4552","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-finding-volume-in-geometry","7":"page_category-math-advertising-group","8":"page_category-volume-and-surface-area","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=4552"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4552\/revisions"}],"predecessor-version":[{"id":95281,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4552\/revisions\/95281"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/99838"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}