{"id":386,"date":"2022-04-13T10:50:41","date_gmt":"2022-04-13T10:50:41","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=386"},"modified":"2025-01-24T11:20:43","modified_gmt":"2025-01-24T11:20:43","slug":"t-6-surface-area-and-volume-of-spheres","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/t-6-surface-area-and-volume-of-spheres\/","title":{"rendered":"T.6 Surface area and volume of spheres"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Surface area and volume of spheres<\/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-aab1813a87ca5577426d6f3ef757ae0c\" style=\"color:#000060\"><strong>Definition of a Sphere<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>A <strong>sphere<\/strong> is a perfectly round 3D object where all points on its surface are equidistant from the center.<\/li>\n\n\n\n<li>It has no edges or vertices.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-000670dfc446c96bf13e010598ed0e66\" style=\"color:#000060\"><strong>Surface Area of a Sphere<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The formula for the surface area of a sphere is:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>A = 4\u03c0r<sup>2<\/sup><\/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><strong>Example Calculation<\/strong>:<br>If the radius of a sphere is 5 cm, then the surface area is:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>A = 4\u03c0 (5)<sup>2<\/sup> = 4\u03c0 (25) = 100\u03c0 \u2248 314.16\u00a0cm<sup>2<\/sup><\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-714ed52434c81b7024549f6affb265e9\" style=\"color:#000060\"><strong>Volume of a Sphere<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The formula for the volume of a sphere is:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">V = 43\u03c0r<sup>3<\/sup><\/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>V = volume<\/li>\n\n\n\n<li>r = radius<\/li>\n\n\n\n<li><strong>Example Calculation<\/strong>:<br>If the radius of a sphere is 6 cm, then the volume is:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">V = 4\/3\u03c0 (6)<sup>3<\/sup> = 4\/3\u03c0 (216) = 864\/3\u03c0 = 288\u03c0 \u2248 904.32\u00a0cm<sup>3<\/sup><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-427590721e2f346ff56a481264f5e72b\" style=\"color:#000060\"><strong>Hemisphere (Half of a Sphere)<\/strong><\/h4>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-36db61b26bf3ca12a57e2cc62d12b170\" style=\"color:#000060\"><strong>Surface Area of a Hemisphere<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Curved surface area<\/strong> (only the curved part):<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong> A = 2\u03c0r<sup>2<\/sup><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Total surface area<\/strong> (curved + circular base): <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>A = 3\u03c0r<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-2c2758f9e4f567f34f9c09c6d366e296\" style=\"color:#000060\"><strong>Volume of a Hemisphere<\/strong>:<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>V = 2\/3\u03c0r<sup>3<\/sup><\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-3aeb5568f2e0defb27665148699c3b45\" style=\"color:#000060\"><strong>Applications of Surface Area and Volume<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Calculating the surface area helps in <strong>painting, wrapping, and covering<\/strong> spherical objects.<\/li>\n\n\n\n<li>Volume calculations are used in <strong>determining the capacity<\/strong> of spherical tanks, balloons, and balls.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-e671c911121d1db367d5ba2fa6f6a07a\" style=\"color:#000060\"><strong>Important Points to Remember<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">Always use the same <strong>units<\/strong> (cm, m, etc.) in calculations.<\/p>\n\n\n\n<p class=\"has-large-font-size\">When solving problems, round off answers <strong>only at the final step<\/strong> for accuracy.<\/p>\n\n\n\n<p class=\"has-large-font-size\">If diameter is given, <strong>radius = diameter \u00f7 2<\/strong>.<\/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:#f2e5a5\"><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 volume of this sphere?<\/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\n<figure class=\"wp-block-image 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-3-2.png\" alt=\"\" class=\"wp-image-10839\" style=\"width:204px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-3-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-3-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-3-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>__________ cubic metres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the radius of the sphere.<\/p>\n\n\n\n<p>radius&nbsp;=&nbsp;7<\/p>\n\n\n\n<p>Use this number in the volume formula. Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14.<\/p>\n\n\n\n<p>volume=4\/3\ud835\udf0br<sup>3<\/sup><\/p>\n\n\n\n<p>\u22484\/3 . 3.14 . 7<sup>3<\/sup><\/p>\n\n\n\n<p>\u22481436.0266<\/p>\n\n\n\n<p>Round your answer to the nearest hundredth:<\/p>\n\n\n\n<p>1,436.0266&nbsp;\u2192&nbsp;1,436.03<\/p>\n\n\n\n<p>The volume of the sphere is about 1,436.03 cubic metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dceadf\"><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 volume of this sphere?<\/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\n<figure class=\"wp-block-image 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-4-3.png\" alt=\"\" class=\"wp-image-10841\" style=\"width:212px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-4-3.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-4-3-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-4-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>___________ cubic centimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the radius of the sphere.<\/p>\n\n\n\n<p>radius&nbsp;=&nbsp;2<\/p>\n\n\n\n<p>Use this number in the volume formula. Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14.<\/p>\n\n\n\n<p>volume=4\/3\ud835\udf0br<sup>3<\/sup><\/p>\n\n\n\n<p>\u22484\/3 . 3.14 . 2<sup>3<\/sup><\/p>\n\n\n\n<p>\u224833.4933<\/p>\n\n\n\n<p>Round your answer to the nearest hundredth:<\/p>\n\n\n\n<p>1,436.0266&nbsp;\u2192&nbsp;1,436.03<\/p>\n\n\n\n<p>The volume of the sphere is about 33.49 cubic centimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f4bef4\"><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 volume of this sphere?<\/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\n<figure class=\"wp-block-image 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-5-1.png\" alt=\"\" class=\"wp-image-10842\" style=\"width:243px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-5-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-5-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-5-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>________ cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the radius of the sphere.<\/p>\n\n\n\n<p>radius&nbsp;=&nbsp;3<\/p>\n\n\n\n<p>Use this number in the volume formula. Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14.<\/p>\n\n\n\n<p>volume=4\/3\ud835\udf0br<sup>3<\/sup><\/p>\n\n\n\n<p>\u22484\/3 . 3.14 . 3<sup>3<\/sup><\/p>\n\n\n\n<p>\u2248113.04<\/p>\n\n\n\n<p>The volume of the sphere is about 113.04 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\/84786\/714\/165\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137.png\" alt=\"\" class=\"wp-image-7409\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137-150x150.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\/260\/508\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-156.png\" alt=\"\" class=\"wp-image-7410\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-156.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-156-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-156-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Surface area and volume of spheres key notes : Definition of a Sphere Surface Area of a Sphere A = 4\u03c0r2 where: A = 4\u03c0 (5)2 = 4\u03c0 (25) = 100\u03c0 \u2248 314.16\u00a0cm2 Volume of a Sphere V = 43\u03c0r3 where: V = 4\/3\u03c0 (6)3 = 4\/3\u03c0 (216) = 864\/3\u03c0 = 288\u03c0 \u2248 904.32\u00a0cm3 Hemisphere<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/t-6-surface-area-and-volume-of-spheres\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.6 Surface area and volume of spheres&#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-386","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/386","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=386"}],"version-history":[{"count":15,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/386\/revisions"}],"predecessor-version":[{"id":17465,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/386\/revisions\/17465"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}