{"id":180,"date":"2022-04-13T08:38:22","date_gmt":"2022-04-13T08:38:22","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=180"},"modified":"2025-02-12T10:41:17","modified_gmt":"2025-02-12T10:41:17","slug":"k-2-surface-area-of-prisms-and-cylinders","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/k-2-surface-area-of-prisms-and-cylinders\/","title":{"rendered":"K.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 has-large-font-size wp-elements-e34077dcebfc97b5ab54c1f20f04bdb2\" style=\"color:#000060\"><strong>Definition of Surface Area<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>The surface area of a 3D shape is the total area of all its faces.<\/li>\n\n\n\n<li>Measured in square units (e.g., cm\u00b2, m\u00b2).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-3691055560086161a183373fa1328ba5\" style=\"color:#000060\"><strong>Surface Area of a Prism<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">A prism is a 3D shape with two parallel and congruent bases.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Surface area (SA) of a prism = <strong>Lateral Surface Area (LSA) + Area of Two Bases<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-644997006131b80d1c0f31e94241921d\" style=\"color:#000060\"><strong>Formula:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>SA = Perimeter\u00a0of\u00a0Base \u00d7 Height + 2 \u00d7 Area\u00a0of\u00a0Base<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-1b747959f08a7b07495a8bd41a6d3e98\" style=\"color:#000060\"><strong>Types of Prisms:<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Rectangular Prism:<\/strong> <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>SA = 2(lw + lh + wh)<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Triangular Prism:<\/strong> <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>SA = (Perimeter \u00d7 Height) + 2 \u00d7 1\/2 \u00d7 Base \u00d7 Height\u00a0of\u00a0Triangle<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-8bf35fd8e6739c36aa07e05ca028901a\" style=\"color:#000060\"><strong>Surface Area of a Cylinder<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">A cylinder has two circular bases and a curved surface.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Formula:<\/strong> SA = 2\u03c0rh + 2\u03c0r<sup>2<\/sup> <\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-ca28fba281bade8f382fcecbbdcaa98c\" style=\"color:#000060\"><strong>where:<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>r = radius of the base<\/li>\n\n\n\n<li>h = height of the cylinder<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">The first term (2\u03c0rh) represents the lateral surface area.<\/p>\n\n\n\n<p class=\"has-large-font-size\">The second term (2\u03c0r<sup>2<\/sup>) accounts for the areas of the two circular bases.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-0bcbf753d4bf9f77214a4e1b00589d26\" style=\"color:#000060\"><strong>Steps to Calculate Surface Area<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Identify the shape (prism or cylinder).<\/li>\n\n\n\n<li>Find the required dimensions (length, width, height, radius, etc.).<\/li>\n\n\n\n<li>Use the appropriate formula.<\/li>\n\n\n\n<li>Solve step by step, ensuring correct units.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-72bc4fe2c9111338294411036d5a4277\" style=\"color:#000060\"><strong>Real-Life Applications<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Prisms:<\/strong> Packaging boxes, aquariums, storage containers.<\/li>\n\n\n\n<li><strong>Cylinders:<\/strong> Cans, pipes, water tanks.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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 loading=\"lazy\" decoding=\"async\" width=\"191\" height=\"156\" 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 loading=\"lazy\" decoding=\"async\" width=\"151\" height=\"123\" 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 decoding=\"async\" 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\"\/><\/figure><\/div>\n\n\n<p>_____ &nbsp;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 decoding=\"async\" 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\"\/><\/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 decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-2.png\" alt=\"\" class=\"wp-image-10809\" style=\"aspect-ratio:1;width:308px;height:auto\"\/><\/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 decoding=\"async\" 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\"\/><\/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\/86042\/246\/126\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66.png\" alt=\"\" class=\"wp-image-7883\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66-150x150.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\/86042\/244\/773\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75.png\" alt=\"\" class=\"wp-image-7884\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75-150x150.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 : Definition of Surface Area Surface Area of a Prism A prism is a 3D shape with two parallel and congruent bases. Surface area (SA) of a prism = Lateral Surface Area (LSA) + Area of Two Bases. Formula: SA = Perimeter\u00a0of\u00a0Base \u00d7 Height + 2 \u00d7<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/k-2-surface-area-of-prisms-and-cylinders\/\">Continue reading <span class=\"screen-reader-text\">&#8220;K.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-180","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/180","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=180"}],"version-history":[{"count":20,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/180\/revisions"}],"predecessor-version":[{"id":16519,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/180\/revisions\/16519"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}