{"id":72916,"date":"2021-02-08T13:36:17","date_gmt":"2021-02-08T08:06:17","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=72916"},"modified":"2021-02-18T13:49:45","modified_gmt":"2021-02-18T08:19:45","slug":"rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/","title":{"rendered":"RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c"},"content":{"rendered":"\n<p>RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c has been provided here. These questions have been prepared with thorough answers by the experts, thus assuring complete accuracy. Basically, the exercises cover the topics of the volume of a sphere. It also covers the topics around the hemisphere and also is based on spherical shells. These solutions are useful for preparing the examinations and enriching their fundamentals. Specifically, the stepwise and detailed analysis of the questions can help understand the underneath concepts.<\/p>\n<p>The surface area and volume of a Sphere Exercise 21.2 do revolve around the following topics like- Volume of a sphere, Volume of a hemisphere, and Volume of a spherical shell.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-21-surface-area-and-volume-of-sphere\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Learn about RD Sharma Class 9 Chapter 21 (Surface Area And Volume of Sphere)<\/strong><\/a><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label 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id=\"item-69d7dc46c3bd9\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/#download-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c21-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-exercise%e2%80%8c-%e2%80%8c212-%e2%80%8csolutions%e2%80%8c-pdf\" title=\"Download RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c PDF\">Download RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/#important-definitions-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c21-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-exercise%e2%80%8c-%e2%80%8c212-%e2%80%8csolutions%e2%80%8c\" title=\"Important Definitions RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c\">Important Definitions RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/#volume-of-a-sphere\" title=\"Volume of a sphere\">Volume of a sphere<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/#volume-of-a-hemisphere\" title=\"Volume of a hemisphere\u00a0\">Volume of a hemisphere\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/#volume-of-a-spherical-shell\" title=\"Volume of a spherical shell\">Volume of a spherical shell<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/#examples-of-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c21-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-exercise%e2%80%8c-%e2%80%8c212-%e2%80%8csolutions%e2%80%8c\" title=\"Examples of RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c\">Examples of RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c21-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-exercise%e2%80%8c-%e2%80%8c212-%e2%80%8csolutions%e2%80%8c-pdf\"><\/span>Download RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Solutions-for-Class-9-Maths-Chapter-21-Surface-Area-and-Volume-of-A-Sphere-Exercise-21.2.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Solutions-for-Class-9-Maths-Chapter-21-Surface-Area-and-Volume-of-A-Sphere-Exercise-21.2.pdf\">Solutions for Class 9 Maths Chapter 21 Surface Area and Volume of A Sphere Exercise 21.2<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c21-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-exercise%e2%80%8c-%e2%80%8c212-%e2%80%8csolutions%e2%80%8c\"><\/span>Important Definitions RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>This exercise of Chapter 21- Surface Area and Volume of Sphere is based on the following topics. Also, know the definitions and formulas with examples below.<\/p>\n<ol>\n<li>Volume of a sphere<\/li>\n<li>Volume of a hemisphere and<\/li>\n<li>Volume of a spherical shell<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"volume-of-a-sphere\"><\/span>Volume of a sphere<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The volume of a sphere is calculated through the formula V=4\/3 \u03c0r3, where \u2018r\u2019 is the radius of the sphere.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"volume-of-a-hemisphere\"><\/span>Volume of a hemisphere\u00a0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The volume of a hemisphere is calculated through formula (2\/3) \u03c0r3 cubic units. Here \u03c0 is a constant which is equal to 3.14 approximately, and \u201cr\u201d is the radius of the hemisphere.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"volume-of-a-spherical-shell\"><\/span>Volume of a spherical shell<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The volume of a Sphere is V = 4\/3\u03c0r\u00b3. When it comes to a spherical shell, the formula becomes V = 4\/3 \u2022 \u03c0 \u2022 (r\u00b3 &#8211; (r-t)\u00b3), where \u2018t\u2019 is the difference between the radius of both.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"examples-of-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c21-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-exercise%e2%80%8c-%e2%80%8c212-%e2%80%8csolutions%e2%80%8c\"><\/span>Examples of RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ques: Find the volume of a sphere whose radius is:<\/strong><\/p>\n<p><strong>(a) 2 cm (b) 3.5 cm (c) 10.5 cm.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>The volume of the sphere = 4\/ 3\u03c0r3 Cubic Units<\/p>\n<p>here, r = radius of a sphere<\/p>\n<p>(a) Radius = 2 cm<\/p>\n<p>Volume = 4\/ 3 \u00d7 22\/ 7 \u00d7 (2) x 3<\/p>\n<p>= 33.52<\/p>\n<p>Volume = 33.52 cm3<\/p>\n<p>(b) Radius = 3.5cm<\/p>\n<p>hence volume = 4\/ 3 \u00d7 22\/ 7 \u00d7 (3.5) x 3<\/p>\n<p>= 179.666<\/p>\n<p>Volume = 179.666 cm3<\/p>\n<p>(c) Radius = 10.5 cm<\/p>\n<p>Volume = 4 \/ 3 \u00d7 22\/ 7 \u00d7 (10.5) x 3<\/p>\n<p>= 4851<\/p>\n<p>Volume = 4851 cm3<\/p>\n<p><strong>Ques: Find the volume of a sphere whose diameter is:<\/strong><\/p>\n<p><strong>(a) 14 cm (b) 3.5 dm (c) 2.1 m<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Volume of the sphere = 4\/ 3\u03c0r3 Cubic Units<\/p>\n<p>here, r = radius of a sphere<\/p>\n<p>(a) diameter = 14 cm<\/p>\n<p>So, radius = diameter \/ 2 = 14\/ 2 = 7cm<\/p>\n<p>Volume = 4\/ 3\u00d7 22\/ 7 \u00d7 (7) x 3<\/p>\n<p>= 1437.33<\/p>\n<p>Volume = 1437.33 cm3<\/p>\n<p>(b) diameter = 3.5 dm<\/p>\n<p>As, radius = diameter \/ 2 = 3.5\/ 2 = 1.75 dm<\/p>\n<p>Volume = 4\/ 3 \u00d7 22\/ 7 \u00d7 (1.75) x 3<\/p>\n<p>= 22.46<\/p>\n<p>Volume = 22.46 dm3<\/p>\n<p>(c) diameter = 2.1 m<\/p>\n<p>As, radius = diameter\/ 2 = 2.1\/ 2 = 1.05 m<\/p>\n<p>Volume = 4\/ 3\u00d7 22\/ 7 \u00d7 (1.05) x 3<\/p>\n<p>= 4.851<\/p>\n<p>Volume = 4.851 m3<\/p>\n<p><strong>Ques: A hemispherical tank has an inner radius of 2.8 m. Find its capacity in liters.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>The radius of the hemispherical tank = 2.8 m<\/p>\n<p>Capacity of the hemispherical tank = 2\/ 3 \u03c0r3<\/p>\n<p>=2\/ 3 \u00d7 22\/ 7 \u00d7 (2.8) x 3 m3<\/p>\n<p>= 45.997 m3<\/p>\n<p>[As 1m3 = 1000 liters]<\/p>\n<p>Hence, capacity in liters = 45997 liters<\/p>\n<p><strong>Ques: How many bullets can be made out of a cube of lead, whose edge measures 22 cm, each bullet being 2 cm in diameter?<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Edge of the cube = 22 cm<\/p>\n<p>Diameter of the bullet = 2 cm<\/p>\n<p>radius of the bullet (r) = 1 cm<\/p>\n<p>Volume of cube = (side)3 = (22)3 cm3 = 10648 cm3<\/p>\n<p>And,<\/p>\n<p>Volume of each bullet which will be spherical in shape = 4\/ 3 \u03c0r3<\/p>\n<p>= 4\/ 3 \u00d722\/ 7 \u00d7(1) x 3 cm3<\/p>\n<p>= 4\/ 3 \u00d722\/ 7 cm3<\/p>\n<p>= 88\/ 21 cm3<\/p>\n<p>Number of bullets = (Volume of the cube)\/ (Volume of the bullet)<\/p>\n<p>= 10648\/ 88\/ 21<\/p>\n<p>= 2541<\/p>\n<p>Therefore, 2541 bullets can be made.<\/p>\n<p><a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Know about CBSE Board<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c has been provided here. These questions have been prepared with thorough answers by the experts, thus assuring complete accuracy. Basically, the exercises cover the topics of the volume of a sphere. It also covers the topics around the hemisphere and also is based on spherical &#8230; <a title=\"RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-21-class-9-maths-exercise-21-2-solutions\/\" aria-label=\"More on RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c21 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c Exercise\u200c \u200c21.2 \u200cSolutions\u200c\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":72923,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411,73410],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72916"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/241"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=72916"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72916\/revisions"}],"predecessor-version":[{"id":75522,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72916\/revisions\/75522"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/72923"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=72916"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=72916"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=72916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}