{"id":388,"date":"2022-04-13T10:50:58","date_gmt":"2022-04-13T10:50:58","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=388"},"modified":"2025-01-24T11:44:23","modified_gmt":"2025-01-24T11:44:23","slug":"t-7-introduction-to-similar-solids","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/t-7-introduction-to-similar-solids\/","title":{"rendered":"T.7 Introduction to similar solids"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Introduction to similar solids<\/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<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b6d26e916aa378dfd9edabe28d4ec4b4\" style=\"color:#000060\"><strong>Definition of Similar Solids<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Two solids are <strong>similar<\/strong> if their corresponding dimensions are proportional and their corresponding angles are equal.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-96efad8d6e2e1cd93754c6f6b7768ba2\" style=\"color:#000060\"><strong>Properties of Similar Solids<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Same shape but different sizes<\/strong><\/li>\n\n\n\n<li><strong>Corresponding linear dimensions are proportional<\/strong><\/li>\n\n\n\n<li><strong>Corresponding angles remain the same<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e54708415bc1b74c089bcaa4244724c1\" style=\"color:#000060\"><strong>Scale Factor<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">The ratio of corresponding linear dimensions (e.g., heights, radii, or side lengths) of two similar solids.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-d0110940a409562d028048e1682b744a\" style=\"color:#000060\"><strong>Ratios of Measurements<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Length Ratio:<\/strong> If the scale factor between two similar solids is <em>k<\/em>, then all corresponding lengths have a ratio of <em>k<\/em>.<\/li>\n\n\n\n<li><strong>Surface Area Ratio:<\/strong> The ratio of surface areas is <strong>k<sup>2<\/sup><\/strong>.<\/li>\n\n\n\n<li><strong>Volume Ratio:<\/strong> The ratio of volumes is <strong>k<sup>3<\/sup><\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-28b9f64bb2d25e29dab832d6d8d60903\" style=\"color:#000060\"><strong>Examples of Similar Solids<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Similar cubes, spheres, cones, cylinders, and pyramids.<\/li>\n\n\n\n<li>Enlarged or reduced 3D models in architecture and engineering.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-2911c724c8990704d25d755832e74ba3\" style=\"color:#000060\"><strong>Real-World Applications<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Model-making in architecture and design.<\/li>\n\n\n\n<li>Scaling up or down objects in engineering and manufacturing.<\/li>\n\n\n\n<li>Understanding relationships in nature (e.g., large and small planets).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8211360026b1f4ce1af25e21a437a48e\" style=\"color:#000060\"><strong>How to Determine if Two Solids are Similar<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Compare corresponding linear dimensions to see if they have a constant ratio.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Check if angles remain the same in corresponding parts of the solids.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Verify surface area and volume ratios using the scale factor.<\/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:#c0f3d4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-08b04588d473e7496a0bb98b9e2de0fa\" style=\"color:#b00012\"><strong>The figures below are similar. What is&nbsp;<em>a<\/em>?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-3.png\" alt=\"\" class=\"wp-image-10857\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-3.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-6-3-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>a = ________millimetres<\/p>\n<\/div><\/div>\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__6_-removebg-preview.png\" alt=\"\" class=\"wp-image-10858\" style=\"width:489px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__6_-removebg-preview.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__6_-removebg-preview-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>Look at the similar figures and find two pairs of corresponding lengths. One pair of corresponding lengths is 2 mm and 4 mm. Another pair of corresponding lengths is 3 mm and&nbsp;<em>a<\/em>.<\/p>\n\n\n\n<p>Use these two pairs of corresponding lengths to set up a proportion and solve for&nbsp;<em>a<\/em>.<\/p>\n\n\n\n<p>2\/4 = 3\/a              Plug in the pairs of corresponding lengths<\/p>\n\n\n\n<p>2\/4 (4 \u00b7 a) = 3\/a (4.a)                       Multiply both sides by (4 \u00b7 a)<\/p>\n\n\n\n<p>2 a=3 \u00b7 4                 Simplify<\/p>\n\n\n\n<p>2 a= 12                  Simplify<\/p>\n\n\n\n<p>2 a \u00f7 2=12 \u00f7 2            Divide both sides by 2<\/p>\n\n\n\n<p>a = 6<\/p>\n\n\n\n<p>The missing length is 6 millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f9c1c1\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-3ed1def96493edb9080b022156c1f8c4\" style=\"color:#b00012\"><strong>The figures below are similar. What is b?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-7-1.png\" alt=\"\" class=\"wp-image-10861\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-7-1.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-7-1-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>b =______ centimetres<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__7_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-10862\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__7_-removebg-preview-3.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__7_-removebg-preview-3-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>Look at the similar figures and find two pairs of corresponding lengths. One pair of corresponding lengths is 5 cm and 10 cm. Another pair of corresponding lengths is 4 cm and&nbsp;<em>b<\/em>.<\/p>\n\n\n\n<p>Use these two pairs of corresponding lengths to set up a proportion and solve for&nbsp;<em>b<\/em>.<\/p>\n\n\n\n<p>5\/10 = 4\/b                Plug in the pairs of corresponding lengths<\/p>\n\n\n\n<p>5\/10 ( 10.b ) = 4\/b ( 10.b )                  Multiply both sides by (10 \u00b7 b)<\/p>\n\n\n\n<p>5b =4 \u00b7 10                  Simplify<\/p>\n\n\n\n<p>5b= 40               Simplify<\/p>\n\n\n\n<p>5b\u00f7 5 = 40 \u00f7 5               Divide both sides by 5<\/p>\n\n\n\n<p>b = 8<\/p>\n\n\n\n<p>The missing length is 8 centimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#fdbde4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-56b8344c1ae4db8500237865c0e88cc0\" style=\"color:#b00012\"><strong>The figures below are similar. What is&nbsp;<em>q<\/em>?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-3.png\" alt=\"\" class=\"wp-image-10864\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-3.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-3-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>q =_______metres<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-4.png\" alt=\"\" class=\"wp-image-10865\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-4.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-4-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>Look at the similar figures and find two pairs of corresponding lengths. One pair of corresponding lengths is 4 m and 3 m. Another pair of corresponding lengths is 8 m and&nbsp;<em>q<\/em>.<\/p>\n\n\n\n<p>Use these two pairs of corresponding lengths to set up a proportion and solve for&nbsp;<em>q<\/em>.<\/p>\n\n\n\n<p>4\/3 = 8\/q               Plug in the pairs of corresponding lengths<\/p>\n\n\n\n<p>4\/3 ( 3.a ) = 8\/q ( 3.q )              Multiply both sides by (3 \u00b7 q)<\/p>\n\n\n\n<p>4q=8 \u00b7 3                    Simplify<\/p>\n\n\n\n<p>4q= 24                    Simplify<\/p>\n\n\n\n<p>4q\u00f7 4=24 \u00f7 4                Divide both sides by 4<\/p>\n\n\n\n<p>q = 6<\/p>\n\n\n\n<p>The missing length is 6 metres.<\/p>\n<\/div><\/div>\n\n\n\n<p><\/p>\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\/014\/610\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138.png\" alt=\"\" class=\"wp-image-7412\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138-150x150.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\/84786\/864\/128\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-157.png\" alt=\"\" class=\"wp-image-7413\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-157.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-157-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-157-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to similar solids key notes : Definition of Similar Solids Properties of Similar Solids Scale Factor Ratios of Measurements Examples of Similar Solids Real-World Applications How to Determine if Two Solids are Similar Compare corresponding linear dimensions to see if they have a constant ratio. Check if angles remain the same in corresponding parts<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/t-7-introduction-to-similar-solids\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.7 Introduction to similar solids&#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-388","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/388","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=388"}],"version-history":[{"count":13,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/388\/revisions"}],"predecessor-version":[{"id":17475,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/388\/revisions\/17475"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}