{"id":178,"date":"2022-04-13T08:38:05","date_gmt":"2022-04-13T08:38:05","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=178"},"modified":"2025-02-12T10:41:18","modified_gmt":"2025-02-12T10:41:18","slug":"k-1-introduction-to-surface-area-and-volume","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/k-1-introduction-to-surface-area-and-volume\/","title":{"rendered":"K.1 Introduction to surface area and volume"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Introduction to surface area and volume<\/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-c78519a4916495e90ab2442d170c60de\" style=\"color:#000060\"><strong>Understanding 3D Shapes<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Three-dimensional (3D) shapes have <strong>length, width, and height<\/strong>.<\/li>\n\n\n\n<li>Common 3D shapes include cubes, cuboids, cylinders, cones, spheres, and pyramids.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-be33fdfd6848fc91c7d604365f499c32\" style=\"color:#000060\"><strong>Surface Area<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Surface area<\/strong> is the total area of all the outer surfaces of a 3D shape.<\/li>\n\n\n\n<li>It is measured in <strong>square units (e.g., cm\u00b2, m\u00b2)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-7b1e7e89a2e5c5b583b9c9b7fdc2c759\" style=\"color:#000060\"><strong>Types of Surface Area:<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Lateral Surface Area (LSA):<\/strong> The area of only the side faces (excluding top and bottom).<\/li>\n\n\n\n<li><strong>Total Surface Area (TSA):<\/strong> The sum of all faces of the shape.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-6f4de823024000d4ada336905427fd3e\" style=\"color:#000060\"><strong>Volume<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>Volume<\/strong> is the space occupied by a 3D shape.<\/p>\n\n\n\n<p class=\"has-large-font-size\">It is measured in <strong>cubic units (e.g., cm\u00b3, m\u00b3)<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-604ba0afc52fa910f5f2c8490003172b\" style=\"color:#000060\"><strong>Formula for Volume:<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Cube: V = a<sup>3<\/sup><\/li>\n\n\n\n<li>Cuboid: V = l \u00d7 w \u00d7 h<\/li>\n\n\n\n<li>Cylinder: V = \u03c0r<sup>2<\/sup> h<\/li>\n\n\n\n<li>Cone: V = 1\/3 \u03c0r<sup>2<\/sup> h<\/li>\n\n\n\n<li>Sphere: V = 4\/3 \u03c0r<sup>3<\/sup><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-d6a262b0a2803512ca5e7e0925bb83bf\" style=\"color:#000060\"><strong>Relationship Between Surface Area and Volume<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Larger surface area allows for more exposure (e.g., heat transfer in objects).<\/li>\n\n\n\n<li>Volume determines the <strong>capacity<\/strong> of an object (e.g., how much liquid a container can hold).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-bb08097df14fdf3903cb769aca6a242c\" 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>Architecture and Construction<\/strong> (e.g., designing buildings and tanks).<\/li>\n\n\n\n<li><strong>Packaging Industry<\/strong> (e.g., determining material for boxes and bottles).<\/li>\n\n\n\n<li><strong>Medical Field<\/strong> (e.g., calculating drug dosage in medicine bottles)<\/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:#bcf9e2\"><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=\"165\" height=\"156\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image.png\" alt=\"\" class=\"wp-image-4104\"\/><\/figure><\/div>\n\n\n<p>______ square metres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Each face of the cube is a square with sides that are 9 metres 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=\"135\" height=\"123\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-1.png\" alt=\"\" class=\"wp-image-4105\" style=\"aspect-ratio:1.0975609756097562;width:199px;height:auto\"\/><\/figure><\/div>\n\n\n<p>area=side . side<\/p>\n\n\n\n<p>      =9 . 9<\/p>\n\n\n\n<p>       =81<\/p>\n\n\n\n<p>The area of each face is 81 square metres. There are 6 faces. Multiply:<\/p>\n\n\n\n<p>surface area=6 . 81<\/p>\n\n\n\n<p>         =486<\/p>\n\n\n\n<p>The surface area of the cube is 486 square metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b1e4fb\"><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-ccf99c0628c4b07d80a5678076b149e1\" style=\"color:#b00012\"><strong>What is the volume?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"208\" height=\"141\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-2.png\" alt=\"\" class=\"wp-image-4107\"\/><\/figure><\/div>\n\n\n<p>&nbsp;&#8212;&#8212;cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the length, width, and height of the rectangular prism.<\/p>\n\n\n\n<p>length: 6 mm<br>width: 9 mm<br>height: 4 mm<\/p>\n\n\n\n<p>Use these numbers in the formula.<\/p>\n\n\n\n<p>volume=length . width . height<\/p>\n\n\n\n<p>            =6 . 9 . 4<\/p>\n\n\n\n<p>            =216<\/p>\n\n\n\n<p>The volume is 216 cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f2b6e2\"><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-ccf99c0628c4b07d80a5678076b149e1\" style=\"color:#b00012\"><strong>What is the volume?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"185\" height=\"156\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-3.png\" alt=\"\" class=\"wp-image-4111\"\/><\/figure><\/div>\n\n\n<p>&#8212;&#8212;cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Each side of the cube is 4 millimetres long. Use the number 4 in the formula.<\/p>\n\n\n\n<p>volume=side . side . side<\/p>\n\n\n\n<p>      =4 .4 . 4<\/p>\n\n\n\n<p>       =64<\/p>\n\n\n\n<p>The volume is 64 cubic millimetres.<\/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\/86041\/705\/792\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-67.png\" alt=\"\" class=\"wp-image-7886\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-67.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-67-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-67-150x150.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\/86041\/699\/180\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-76.png\" alt=\"\" class=\"wp-image-7887\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-76.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-76-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-76-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to surface area and volume key notes : Understanding 3D Shapes Surface Area Types of Surface Area: Volume Volume is the space occupied by a 3D shape. It is measured in cubic units (e.g., cm\u00b3, m\u00b3). Formula for Volume: Relationship Between Surface Area and Volume Real-Life Applications Learn with an example What is the<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/k-1-introduction-to-surface-area-and-volume\/\">Continue reading <span class=\"screen-reader-text\">&#8220;K.1 Introduction to surface area and volume&#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-178","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178","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=178"}],"version-history":[{"count":19,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178\/revisions"}],"predecessor-version":[{"id":16521,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178\/revisions\/16521"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}