{"id":392,"date":"2022-04-13T10:51:30","date_gmt":"2022-04-13T10:51:30","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=392"},"modified":"2025-01-24T11:45:22","modified_gmt":"2025-01-24T11:45:22","slug":"t-9-surface-area-and-volume-review","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/t-9-surface-area-and-volume-review\/","title":{"rendered":"T.9 Surface area and volume review"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Surface area and volume review<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-28d136ae4331e7eb05ec8e1cb71ebcde\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9ba9b0f4d3aa510a945f17bd235f7459\" style=\"color:#000060\"><strong>Surface Area<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Surface area is the total area of all the faces of a three-dimensional shape.<\/p>\n\n\n\n<p class=\"has-large-font-size\">It is measured in square units (e.g., cm\u00b2, m\u00b2).<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-3aaf8db929967315323216c4e323bc5c\" style=\"color:#000060\"><strong>Formulas for Surface Area:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Cube:<\/strong> 6s<sup>2<\/sup> (where sss is the side length)<\/li>\n\n\n\n<li><strong>Rectangular Prism:<\/strong> 2(lw+lh+wh) (where l,w,h are length, width, and height)<\/li>\n\n\n\n<li><strong>Sphere:<\/strong> 4\u03c0r<sup>2<\/sup> (where r is the radius)<\/li>\n\n\n\n<li><strong>Cylinder:<\/strong> 2\u03c0r2+2\u03c0rh (where r is radius, h is height)<\/li>\n\n\n\n<li><strong>Cone:<\/strong> \u03c0r<sup>2<\/sup>+\u03c0rl (where r is radius, l is slant height)<\/li>\n\n\n\n<li><strong>Pyramid:<\/strong> B+1\/2Pl (where B is the base area, P is the perimeter of the base, and l is slant height)<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Volume<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">Volume is the amount of space occupied by a three-dimensional object.<\/p>\n\n\n\n<p class=\"has-large-font-size\">It is measured in cubic units (e.g., cm\u00b3, m\u00b3).<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-f57f53c35ce5fa5fb04e667f3ddc7af2\" style=\"color:#000060\"><strong>Formulas for Volume:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Cube:<\/strong> s<sup>3<\/sup><\/li>\n\n\n\n<li><strong>Rectangular Prism:<\/strong> lwh<\/li>\n\n\n\n<li><strong>Sphere:<\/strong> 4\/3\u03c0r<sup>3<\/sup><\/li>\n\n\n\n<li><strong>Cylinder:<\/strong> \u03c0r<sup>2<\/sup>h<\/li>\n\n\n\n<li><strong>Cone:<\/strong> 1\/3 \u03c0r<sup>2<\/sup>h<\/li>\n\n\n\n<li><strong>Pyramid:<\/strong> 1\/3 Bh<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-cc99680ca991f7ff9a1e335af9a337a2\" style=\"color:#000060\"><strong>Relationship Between Surface Area and Volume<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Surface area affects how fast an object exchanges heat or dissolves.<\/li>\n\n\n\n<li>Volume determines the capacity of an object.<\/li>\n\n\n\n<li>As an object increases in size, volume grows faster than surface area.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-0351598603d1f75c760c056c5d3b7199\" style=\"color:#000060\"><strong>Problem-Solving Tips<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">Identify the shape and use the correct formula.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Ensure correct unit conversions (e.g., cm\u00b2 to m\u00b2, cm\u00b3 to liters).<\/p>\n\n\n\n<p class=\"has-large-font-size\">Break complex shapes into simpler parts.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Use \u03c0 \u2248 3.14 when necessary.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Check if the problem requires total or lateral surface area.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f3afaf\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p> \ud83d\udcda What is the surface area of this sphere?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5060e8c06e6628b9ce00faeabe7e8ccc\" style=\"color:#b00012\"><strong>\ud83d\udcda Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14 and round your answer to the nearest hundredth.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"185\" height=\"195\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-500px-25.png\" alt=\"\" class=\"wp-image-4254\"\/><\/figure>\n\n\n\n<p>_______square centimetres<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the radius of the sphere.radius&nbsp;=&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>12&nbsp;\u00d7&nbsp;diameter<\/td><td>&nbsp;=&nbsp;<\/td><td>12&nbsp;\u00d7&nbsp;14&nbsp;=&nbsp;7<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use this number in the surface area formula. Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14.<\/li>\n\n\n\n<li>Surface area&nbsp;=&nbsp;4\u200b\ud835\udf0b<em>r<\/em><sup>2<\/sup><\/li>\n\n\n\n<li>&nbsp;\u2248&nbsp;4 \u00d7 3.14 \u00d7&nbsp;7<sup>2<\/sup><\/li>\n\n\n\n<li>&nbsp;\u2248&nbsp;615.44The surface area of the sphere is about 615.44 square centimetres.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bfb9fd\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-c6d59952e3fde567b2cfec7133ca9a2c\" style=\"color:#b00012\"><strong> \ud83d\udcda What is the volume?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-3-3.png\" alt=\"\" class=\"wp-image-10906\" style=\"aspect-ratio:1.6706586826347305;width:379px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-3-3.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-3-3-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>________ cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the base, height, and length of the triangular prism.<\/li>\n\n\n\n<li>base:&nbsp;12 mm<br>height:&nbsp;7 mm<br>length:&nbsp;6 mm<br>Use these numbers in the volume formula.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Volume<\/td><td>&nbsp;=&nbsp;<\/td><td>12&nbsp;\u00d7&nbsp;base&nbsp;\u00d7&nbsp;height&nbsp;\u00d7&nbsp;length<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>12&nbsp;\u00d7&nbsp;12&nbsp;\u00d7&nbsp;7&nbsp;\u00d7&nbsp;6<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>252<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The volume is 252 cubic millimetres.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bdf9e9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p> \ud83d\udcda The surface area of this cone is 414.48 square millimetres. What is the slant height of this cone?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5060e8c06e6628b9ce00faeabe7e8ccc\" style=\"color:#b00012\"><strong>\ud83d\udcda Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14 and round your answer to the nearest hundredth.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-2-5.png\" alt=\"\" class=\"wp-image-10905\" style=\"aspect-ratio:1.09;width:294px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-2-5.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-2-5-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-2-5-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>s \u2248&nbsp;_______ millimetres<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the surface area and radius of the cone.<br>surface area&nbsp;=&nbsp;414.48<br>radius&nbsp;=&nbsp;6<br>Find the area of the base. Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14.<br>Area of base&nbsp;=&nbsp;\u200b\ud835\udf0b<em>r<\/em><sup>2<\/sup><br>&nbsp;\u2248&nbsp;3.14 \u00d7&nbsp;6<sup>2<\/sup><br>&nbsp;\u2248&nbsp;113.04<\/li>\n\n\n\n<li>Find the lateral area.<br>Lateral area&nbsp;=&nbsp;\u200b\ud835\udf0b<em>rs<\/em><br>&nbsp;\u2248&nbsp;3.14 \u00d7 6 \u00d7&nbsp;<em>s<\/em><br>&nbsp;\u2248&nbsp;18.84<em>s<\/em><\/li>\n\n\n\n<li>Now add the areas to find the slant height of the cone.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677129454966_330\" class=\"wp-block-table\"><table><tbody><tr><td>Surface area<\/td><td>&nbsp;=&nbsp;<\/td><td><em>B<\/em>&nbsp;+&nbsp;<em>L.A.<\/em><\/td><\/tr><tr><td><\/td><\/tr><tr><td>414.48<\/td><td>&nbsp;\u2248&nbsp;<\/td><td>113.04 + 18.84<em>s<\/em><\/td><\/tr><tr><td><\/td><\/tr><tr><td>414.48 \u2212 113.04<\/td><td>&nbsp;\u2248&nbsp;<\/td><td>18.84<em>s<\/em><\/td><\/tr><tr><td><\/td><\/tr><tr><td>301.44<\/td><td>&nbsp;\u2248&nbsp;<\/td><td>18.84<em>s<\/em><\/td><\/tr><tr><td><\/td><\/tr><tr><td>301.44 \u00f7 18.84<\/td><td>&nbsp;\u2248&nbsp;<\/td><td><em>s<\/em><\/td><\/tr><tr><td><\/td><\/tr><tr><td>16<\/td><td>&nbsp;\u2248&nbsp;<\/td><td><em>s<\/em><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The slant height of the cone is about 16 millimetres.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84787\/955\/906\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-140.png\" alt=\"\" class=\"wp-image-7418\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-140.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-140-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-140-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84787\/741\/644\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-159.png\" alt=\"\" class=\"wp-image-7419\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-159.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-159-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-159-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Surface area and volume review key notes : Surface Area Surface area is the total area of all the faces of a three-dimensional shape. It is measured in square units (e.g., cm\u00b2, m\u00b2). Formulas for Surface Area: Volume Volume is the amount of space occupied by a three-dimensional object. It is measured in cubic units<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/t-9-surface-area-and-volume-review\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.9 Surface area and volume review&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-392","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/392","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=392"}],"version-history":[{"count":12,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/392\/revisions"}],"predecessor-version":[{"id":17477,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/392\/revisions\/17477"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=392"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}