{"id":69058,"date":"2021-08-27T21:04:00","date_gmt":"2021-08-27T15:34:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69058"},"modified":"2023-11-28T10:48:47","modified_gmt":"2023-11-28T05:18:47","slug":"rd-sharma-solutions-class-12-maths-chapter-13-exercise-13-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-13-exercise-13-1\/","title":{"rendered":"RD Sharma Class 12 Solutions Chapter 13 Derivative as a Rate Measurer Exercise 13.1 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-120629\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-13-Exercise-13.1.jpg\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-13-Exercise-13.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-13-Exercise-13.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1:\u00a0<\/strong>The first exercise in Chapter 13 is about calculating the derivative of a function to use as a rate measurer. These <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-12-solutions\/\"><strong>RD Sharma Class 12 Solutions<\/strong><\/a> are created in an interactive manner by Kopykitab&#8217;s experts in order to excite students&#8217; interest in studying. It also includes explanatory illustrations and tables for comparison study, making it simple to grasp the most important concepts. Students who are having trouble solving these topics could check <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-13-derivative-as-a-rate-measurer\/\"><strong>RD Sharma Solutions for Class 12 Maths Chapter 13<\/strong><\/a> of <strong>Exerci<\/strong><strong>s<\/strong><strong>e 13.1<\/strong> for assistance. These solutions will be quite beneficial to them.<\/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 for=\"item-69ef23ff50c68\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69ef23ff50c68\"><\/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-solutions-class-12-maths-chapter-13-exercise-13-1\/#download-rd-sharma-solutions-class-12-maths-chapter-13-exercise-131-free-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1 Free PDF\">Download RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1 Free PDF<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-13-exercise-13-1\/#access-answers-to-maths-rd-sharma-solutions-for-class-12-chapter-13-%e2%80%93-derivative-as-a-rate-measurer-exercise-131-important-questions-with-solution\" title=\"Access answers to Maths RD Sharma Solutions For Class 12 Chapter 13 \u2013 Derivative as a Rate Measurer Exercise 13.1 Important Questions With Solution\">Access answers to Maths RD Sharma Solutions For Class 12 Chapter 13 \u2013 Derivative as a Rate Measurer Exercise 13.1 Important Questions With Solution<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-13-exercise-13-1\/#faqs-on-rd-sharma-class-12-solutions-chapter-13-exercise-131\" title=\"FAQs on RD Sharma Class 12 Solutions Chapter 13 Exercise 13.1\">FAQs on RD Sharma Class 12 Solutions Chapter 13 Exercise 13.1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-13-exercise-13-1\/#are-the-rd-sharma-solutions-for-class-12-maths-chapter-13-exercise-131-considered-as-the-best-study-material-for-board-exam-preparation\" title=\"Are the RD Sharma Solutions for Class 12 Maths Chapter 13 Exercise 13.1 considered as the best study material for board exam preparation?\">Are the RD Sharma Solutions for Class 12 Maths Chapter 13 Exercise 13.1 considered as the best study material for board exam preparation?<\/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-solutions-class-12-maths-chapter-13-exercise-13-1\/#where-can-i-get-rd-sharma-class-12-maths-solutions-chapter-13-exercise-131-free-pdf\" title=\"Where can I get RD Sharma Class 12 Maths Solutions Chapter 13 Exercise 13.1 Free PDF?\">Where can I get RD Sharma Class 12 Maths Solutions Chapter 13 Exercise 13.1 Free PDF?<\/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-solutions-class-12-maths-chapter-13-exercise-13-1\/#how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-13-exercise-131\" title=\"How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1?\">How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-13-exercise-131-free-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1 Free 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: 800px;}<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\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-13-Ex-13.1-1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-13-Ex-13.1-1.pdf\">RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-maths-rd-sharma-solutions-for-class-12-chapter-13-%e2%80%93-derivative-as-a-rate-measurer-exercise-131-important-questions-with-solution\"><\/span>Access answers to Maths RD Sharma Solutions For Class 12 Chapter 13 \u2013 Derivative as a Rate Measurer Exercise 13.1 Important Questions With Solution<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm9.staticflickr.com\/8650\/16045452109_31efe30151_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q1\" width=\"308\" height=\"216\" \/><\/p>\n<p><strong>2. Find the rate of change of the volume of a sphere with respect to its diameter.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7544\/16229704901_a0fa67319d_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q2\" width=\"370\" height=\"312\" \/><\/p>\n<p><strong>3. Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2 cm.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm9.staticflickr.com\/8651\/16045452029_bdb012c279_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q3\" width=\"329\" height=\"405\" \/><\/p>\n<p><strong>4. Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7568\/15611718813_ffa22cf471_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q4\" width=\"329\" height=\"385\" \/><\/p>\n<p><strong>Derivatives as a Rate Measurer Ex 13.1 Q5<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8677\/15609158194_4b197ec1bf_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q5\" width=\"416\" height=\"113\" \/><br \/><strong>Derivatives as a Rate Measurer Ex 13.1 Q6<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7495\/16230757542_6d96e63e3d_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q6\" width=\"286\" height=\"203\" \/><br \/><strong>Derivatives as a Rate Measurer Ex 13.1 Q7<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7556\/16229704781_b10e424755_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q7\" width=\"168\" height=\"196\" \/><br \/><strong>Derivatives as a Rate Measurer Ex 13.1 Q8<\/strong><img src=\"https:\/\/farm9.staticflickr.com\/8604\/15609159014_af3c9a69fa_o.gif\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q8\" width=\"454\" height=\"351\" \/><br \/><strong>Derivatives as a Rate Measurer Ex 13.1 Q9<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7529\/16044060938_9319724cc3_o.gif\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q9\" width=\"620\" height=\"216\" \/><br \/><strong>Derivatives as a Rate Measurer Ex 13.1 Q10<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/3\/2044\/32833412115_388af212b1_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 13 Derivatives as a Rate Measurer Ex 13.1 Q10\" width=\"536\" height=\"207\" \/><\/p>\n<p>We have provided complete details of RD Sharma Solutions for Class 12 Maths Chapter 13 Exercise 13.1. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-12-solutions-chapter-13-exercise-131\"><\/span>FAQs on RD Sharma Class 12 Solutions Chapter 13 Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630064706698\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-the-rd-sharma-solutions-for-class-12-maths-chapter-13-exercise-131-considered-as-the-best-study-material-for-board-exam-preparation\"><\/span>Are the RD Sharma Solutions for Class 12 Maths Chapter 13 Exercise 13.1 considered as the best study material for board exam preparation?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The RD Sharma Solutions have been developed in accordance with the most recent CBSE guidelines and syllabus. To help students ace the exam, all of the solutions are crafted by individual subject matter experts.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630064748609\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-rd-sharma-class-12-maths-solutions-chapter-13-exercise-131-free-pdf\"><\/span>Where can I get RD Sharma Class 12 Maths Solutions Chapter 13 Exercise 13.1 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630064791793\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-13-exercise-131\"><\/span>How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 10 questions in RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 13 Exercise 13.1:\u00a0The first exercise in Chapter 13 is about calculating the derivative of a function to use as a rate measurer. These RD Sharma Class 12 Solutions are created in an interactive manner by Kopykitab&#8217;s experts in order to excite students&#8217; interest in studying. It also includes &#8230; <a title=\"RD Sharma Class 12 Solutions Chapter 13 Derivative as a Rate Measurer Exercise 13.1 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-13-exercise-13-1\/\" aria-label=\"More on RD Sharma Class 12 Solutions Chapter 13 Derivative as a Rate Measurer Exercise 13.1 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":120629,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3429,73223,73664,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69058"}],"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\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=69058"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69058\/revisions"}],"predecessor-version":[{"id":513215,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69058\/revisions\/513215"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/120629"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69058"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69058"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69058"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}