{"id":380,"date":"2022-04-13T10:49:54","date_gmt":"2022-04-13T10:49:54","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=380"},"modified":"2025-01-22T10:34:04","modified_gmt":"2025-01-22T10:34:04","slug":"t-3-surface-area-of-cones","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/t-3-surface-area-of-cones\/","title":{"rendered":"T.3 Surface area of cones"},"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 cones<\/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-8f0e9d9c5daaa1c7c095d7e98da4d9b6\" style=\"color:#000060\"><strong>Definition of a Cone<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">A cone is a three-dimensional geometric shape with a circular base and a curved surface that tapers to a single point (the apex).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-ad5d9ac7dd205547f536f84dc5fffed4\" style=\"color:#000060\"><strong>Surface Area of a Cone<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">The total surface area of a cone includes two parts:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Curved Surface Area (CSA)<\/strong><\/li>\n\n\n\n<li><strong>Total Surface Area (TSA)<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b63d33383ff4cbdd68f98f6b4743db65\" style=\"color:#000060\"><strong>Curved Surface Area (CSA) Formula<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>CSA = \u03c0rl<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Where:<\/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>l = Slant height<\/li>\n\n\n\n<li>\u03c0 \u2248 3.1416<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b596ecd31f2ae3580922d9f9cb1f8881\" style=\"color:#000060\"><strong>Total Surface Area (TSA) Formula<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>TSA = \u03c0rl + \u03c0r<sup>2<\/sup><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">This includes the curved surface area plus the area of the circular base.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e102fd8725186135cf66051a09c87456\" style=\"color:#000060\"><strong>Finding Slant Height (l)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The slant height l can be calculated using the Pythagorean theorem: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>l = \u221ar<sup>2 <\/sup>+ h<sup>2<\/sup><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Where hhh is the vertical height of the cone.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b5c62f987da57d79cb1f1b7aec9e8d38\" style=\"color:#000060\"><strong>Units of Measurement<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Surface area is measured in <strong>square units<\/strong> (e.g., cm\u00b2, m\u00b2).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5f2a1c55076ba157419eb04926947c6f\" style=\"color:#000060\"><strong>Real-Life Applications<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Used in designing ice cream cones, funnels, party hats, and architectural structures like domes.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-2b3d22baa413cebb20927420237c16a2\" style=\"color:#000060\"><strong>Key Concept<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">The curved surface is a <strong>sector<\/strong> of a circle when unfolded.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-cb7bf5938c80e2102a4292daca7c1cc3\" style=\"color:#000060\"><strong>Common Mistakes to Avoid<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Confusing slant height lll with vertical height hhh.<\/li>\n\n\n\n<li>Forgetting to add the base area when finding TSA.<\/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:#f9dcc0\"><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>What is the surface area of this cone?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aceb31132f26cef0978b33376694437e\" style=\"color:#b00012\"><strong>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 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-8-2.png\" alt=\"\" class=\"wp-image-10819\" style=\"width:372px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-8-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>______ &nbsp;square metres<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the radius and slant height of the cone.<\/p>\n\n\n\n<p>radius=1\/2 . diameter=1\/2 . 6=3<\/p>\n\n\n\n<p>slant height=8<\/p>\n\n\n\n<p>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;3<sup>2<\/sup><br>                    &nbsp;\u2248&nbsp;28.26 <\/p>\n\n\n\n<p>Find the lateral area.<br>Lateral area&nbsp;=&nbsp;\u200b\ud835\udf0b<em>rs<\/em><br>&nbsp;                   \u2248&nbsp;3.14 \u00d7 3 \u00d7 8<br>&nbsp;                   \u2248&nbsp;75.36<\/p>\n\n\n\n<p>Now add the areas to find the surface area of the cone.<br>Surface area&nbsp;=&nbsp;area of base + lateral area<br>&nbsp;                   \u2248&nbsp;28.26 + 75.36<br>&nbsp;                  \u2248&nbsp;103.62<\/p>\n\n\n\n<p>The surface area of the cone is about 103.62 square metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bdfbf7\"><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>What is the surface area of this cone?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aceb31132f26cef0978b33376694437e\" style=\"color:#b00012\"><strong>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 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-9-3.png\" alt=\"\" class=\"wp-image-10820\" style=\"width:372px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-9-3.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-9-3-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-9-3-150x150.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 radius and slant height of the cone.<\/p>\n\n\n\n<p>radius=1\/2 . diameter=1\/2 . 2=1<\/p>\n\n\n\n<p>slant height=3<\/p>\n\n\n\n<p>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;1<sup>2<\/sup><br>&nbsp;                   \u2248&nbsp;3.14<\/p>\n\n\n\n<p>Find the lateral area.<br>Lateral area&nbsp;=&nbsp;\u200b\ud835\udf0b<em>r<\/em><em>s<\/em><br>&nbsp;                 \u2248&nbsp;3.14 \u00d7 1 \u00d7 3<br>&nbsp;                 \u2248&nbsp;9.42<\/p>\n\n\n\n<p>Now add the areas to find the surface area of the cone.<br>Surface area&nbsp;=&nbsp;area of base + lateral area<br>&nbsp;                   \u2248&nbsp;3.14 + 9.42<br>                   &nbsp;\u2248&nbsp;12.56<\/p>\n\n\n\n<p>The surface area of the cone is about 12.56 square metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#feb0b0\"><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>What is the surface area of this cone?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aceb31132f26cef0978b33376694437e\" style=\"color:#b00012\"><strong>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 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-10-1.png\" alt=\"\" class=\"wp-image-10821\" style=\"width:365px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-10-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-10-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-10-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_____square centimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the radius and slant height of the cone.<\/p>\n\n\n\n<p>radius&nbsp;=&nbsp;5<br>slant height&nbsp;=&nbsp;10<\/p>\n\n\n\n<p><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;5<sup>2<\/sup><br>&nbsp;                   \u2248&nbsp;78.5<\/p>\n\n\n\n<p>Find the lateral area.<br>Lateral area&nbsp;=&nbsp;\u200b\ud835\udf0b<em>r<\/em><em>s<\/em><br>&nbsp;                   \u2248&nbsp;3.14 \u00d7 5 \u00d7 10<br>                 &nbsp;\u2248&nbsp;157<\/p>\n\n\n\n<p>Now add the areas to find the surface area of the cone.<br>Surface area&nbsp;=&nbsp;area of base + lateral area<br>&nbsp;                  \u2248&nbsp;78.5 + 157<br>&nbsp;                 \u2248&nbsp;235.5<\/p>\n\n\n\n<p>The surface area of the cone is about 235.50 square centimetres.<\/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\/84598\/133\/846\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134.png\" alt=\"\" class=\"wp-image-7400\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134-150x150.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\/84770\/940\/677\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-153.png\" alt=\"\" class=\"wp-image-7401\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-153.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-153-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-153-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Surface area of cones key notes : Definition of a Cone Surface Area of a Cone The total surface area of a cone includes two parts: Curved Surface Area (CSA) Formula CSA = \u03c0rl Where: Total Surface Area (TSA) Formula TSA = \u03c0rl + \u03c0r2 Finding Slant Height (l) l = \u221ar2 + h2 Units<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/t-3-surface-area-of-cones\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.3 Surface area of cones&#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-380","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/380","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=380"}],"version-history":[{"count":12,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/380\/revisions"}],"predecessor-version":[{"id":17441,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/380\/revisions\/17441"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=380"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}