{"id":378,"date":"2022-04-13T10:49:36","date_gmt":"2022-04-13T10:49:36","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=378"},"modified":"2025-01-24T10:47:46","modified_gmt":"2025-01-24T10:47:46","slug":"t-2-surface-area-of-prisms-and-cylinders","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/t-2-surface-area-of-prisms-and-cylinders\/","title":{"rendered":"T.2 Surface area of prisms and cylinders"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Surface area of prisms and cylinders<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-203290aba75681a4fb07a0852f132b50\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-cca04506b10c42be836d830bbbb261ef\" style=\"color:#000060\"><strong>Surface Area Basics<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Surface area is the total area of all the faces of a 3D shape.<\/li>\n\n\n\n<li>It is measured in <strong>square units<\/strong> (e.g., cm\u00b2, m\u00b2).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-3578bf5223122a6f523be8e08684b040\" style=\"color:#000060\"><strong>Surface Area of Prisms<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">A <strong>prism<\/strong> is a 3D shape with two <strong>identical<\/strong> parallel bases and rectangular or parallelogram lateral faces.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Formula for Surface Area of a Prism:<\/strong> <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>Surface&nbsp;Area = 2 \u00d7 Base&nbsp;Area + Lateral&nbsp;Area<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Lateral Area<\/strong> is the sum of the areas of all the side faces (excluding the bases).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-52aaf445534c689590cff6b9b66e58da\" style=\"color:#000060\"><strong>Example:<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">For a rectangular prism (cuboid) with <strong>length (l), width (w), and height (h)<\/strong>:<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">Surface&nbsp;Area = 2(lw + lh + wh)<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-f9a3ceccf296c3afedd4dc59b16592a3\" style=\"color:#000060\"><strong>Surface Area of Cylinders<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">A <strong>cylinder<\/strong> has two circular bases and a curved lateral surface.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5aee49a81a3906354c3ba540f87d6958\" style=\"color:#000060\"><strong>Formula for Surface Area of a Cylinder:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">Surface&nbsp;Area = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-46d4850bcb9ae0d22d8f0324f38dd33c\" style=\"color:#000060\"><strong>Where:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>r = radius of the base<\/li>\n\n\n\n<li>h = height of the cylinder<\/li>\n\n\n\n<li>2\u03c0r<sup>2<\/sup> = total area of the two circular bases<\/li>\n\n\n\n<li>2\u03c0rh<sup>2<\/sup> = lateral (curved) surface area<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-701304112425e0f663da9b7fc3661359\" style=\"color:#000060\"><strong>Key Steps to Find Surface Area<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Identify the <strong>shape<\/strong> (prism or cylinder).<\/li>\n\n\n\n<li>Determine the <strong>dimensions<\/strong> (length, width, height, radius, etc.).<\/li>\n\n\n\n<li>Calculate the <strong>base area<\/strong> and <strong>lateral area<\/strong> separately.<\/li>\n\n\n\n<li>Add all the areas to get the <strong>total surface area<\/strong>.<\/li>\n<\/ul>\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:#b8f3b8\"><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-771a824863627ce1eac5207b9e7797db\" style=\"color:#b00012\"><strong>What is the surface area?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-4.png\" alt=\"\" class=\"wp-image-4114\"\/><\/figure><\/div>\n\n\n<p>_____ square centimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Each face of the cube is a square with sides that are 10 centimetres long.<\/p>\n\n\n\n<p>Find the area of one face:<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-5.png\" alt=\"\" class=\"wp-image-4115\"\/><\/figure><\/div>\n\n\n<p>side = 10 cm<\/p>\n\n\n\n<p>area = side . side<\/p>\n\n\n\n<p>= 10 . 10<\/p>\n\n\n\n<p>= 100<\/p>\n\n\n\n<p>The area of each face is 100 square centimetres. There are 6 faces. Multiply:<\/p>\n\n\n\n<p>surface area = 6 . 100<\/p>\n\n\n\n<p>= 600<\/p>\n\n\n\n<p>The surface area of the cube is 600 square centimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bdacf8\"><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-771a824863627ce1eac5207b9e7797db\" style=\"color:#b00012\"><strong>What is the surface area?<\/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-4-2.png\" alt=\"\" class=\"wp-image-10807\" style=\"width:299px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-4-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-4-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-4-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_____ square millimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>Each face of the cube is a square with sides that are 2 millimetres long.<\/p>\n\n\n\n<p>Find the area of one face:<\/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__5_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-10808\" style=\"width:214px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__5_-removebg-preview-3.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__5_-removebg-preview-3-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__5_-removebg-preview-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Area = side \u00d7 side<\/p>\n\n\n\n<p>= 2 \u00d7 2<\/p>\n\n\n\n<p>= 4<\/p>\n\n\n\n<p>The area of each face is 4 square millimetres. There are 6 faces. Multiply:<\/p>\n\n\n\n<p>Surface area = 6 \u00d7 4<\/p>\n\n\n\n<p>= 24<\/p>\n\n\n\n<p>The surface area of the cube is 24 square millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f8c2c2\"><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-771a824863627ce1eac5207b9e7797db\" style=\"color:#b00012\"><strong>What is the surface area?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-2.png\" alt=\"\" class=\"wp-image-10809\" style=\"width:246px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_____ square metres<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the area of the faces in each pair.<\/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__7_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-10811\" style=\"width:442px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__7_-removebg-preview-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__7_-removebg-preview-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__7_-removebg-preview-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Now add the areas of the 6 faces.<br>Surface area<br>= 21 + 21 + 35 + 35 + 15 + 15<\/p>\n\n\n\n<p>= 142<\/p>\n\n\n\n<p>The surface area of the rectangular prism is 142 square metres.<\/p>\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\/84595\/044\/585\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133.png\" alt=\"\" class=\"wp-image-7397\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133-150x150.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\/84616\/657\/552\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-152.png\" alt=\"\" class=\"wp-image-7398\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-152.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-152-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-152-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Surface area of prisms and cylinders key notes : Surface Area Basics Surface Area of Prisms A prism is a 3D shape with two identical parallel bases and rectangular or parallelogram lateral faces. Surface&nbsp;Area = 2 \u00d7 Base&nbsp;Area + Lateral&nbsp;Area Example: For a rectangular prism (cuboid) with length (l), width (w), and height (h): Surface&nbsp;Area<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/t-2-surface-area-of-prisms-and-cylinders\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.2 Surface area of prisms and cylinders&#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-378","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/378","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=378"}],"version-history":[{"count":15,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/378\/revisions"}],"predecessor-version":[{"id":17460,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/378\/revisions\/17460"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}