{"id":156343,"date":"2023-08-30T14:03:16","date_gmt":"2023-08-30T08:33:16","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156343"},"modified":"2023-08-30T14:03:59","modified_gmt":"2023-08-30T08:33:59","slug":"a-parabola-x-y2-with-0-x-1-is-shown-in-the-figure-the-volume-of-the-solid-of-rotation-obtained-by-rotating-the-shaded-area-by-360-around-the-x-axis-is","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-parabola-x-y2-with-0-x-1-is-shown-in-the-figure-the-volume-of-the-solid-of-rotation-obtained-by-rotating-the-shaded-area-by-360-around-the-x-axis-is\/","title":{"rendered":"A parabola x = y2 with 0 \u00a3 x \u00a3 1 is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360\u00b0 around the x-axis is"},"content":{"rendered":"\n<p>Q. <span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt;\nfont-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">A parabola<span style=\"letter-spacing:.05pt\"> <\/span><i>x <\/i><\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt;\nfont-family:Symbol;mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:\n&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:EN-US;\nmso-bidi-language:AR-SA\">=<\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:\n11.0pt;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\"> <i>y<\/i><sup>2<\/sup><span style=\"letter-spacing:\n.05pt\"> <\/span>with 0 <\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:\n11.0pt;font-family:Symbol;mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:\n&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:EN-US;\nmso-bidi-language:AR-SA\">\u00a3<\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:\n11.0pt;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\"> <i>x <\/i><\/span><span style=\"font-size:12.0pt;\nmso-bidi-font-size:11.0pt;font-family:Symbol;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:\nEN-US;mso-bidi-language:AR-SA\">\u00a3<\/span><span style=\"font-size:12.0pt;\nmso-bidi-font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:EN-US;\nmso-bidi-language:AR-SA\"> 1 is shown in the figure. The volume of the solid of rotation<span style=\"letter-spacing:-2.85pt\"> <\/span>obtained by<span style=\"letter-spacing:-.15pt\"> <\/span>rotating<span style=\"letter-spacing:-.15pt\"> <\/span>the<span style=\"letter-spacing:-.05pt\"> <\/span>shaded area<span style=\"letter-spacing:-.05pt\"> <\/span>by<span style=\"letter-spacing:-.25pt\"> <\/span>360<b>\u00b0<span style=\"letter-spacing:.1pt\"> <\/span><\/b>around the <i>x<\/i>-axis is<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/image-54.png\" alt=\"\" class=\"wp-image-156344\" style=\"width:257px;height:181px\" width=\"257\" height=\"181\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/image-54.png 408w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/image-54-300x211.png 300w\" sizes=\"auto, (max-width: 257px) 100vw, 257px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"546\" height=\"142\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-638.png\" alt=\"\" class=\"wp-image-156345\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-638.png 546w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-638-300x78.png 300w\" sizes=\"auto, (max-width: 546px) 100vw, 546px\" \/><\/figure>\n\n\n\n<p>Ans: \u03c0\/2<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"267\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-639.png\" alt=\"\" class=\"wp-image-156346\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. A parabola x = y2 with 0 \u00a3 x \u00a3 1 is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360\u00b0 around the x-axis is Ans: \u03c0\/2 Sol:<\/p>\n","protected":false},"author":419,"featured_media":156347,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-156343","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156343","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=156343"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156343\/revisions"}],"predecessor-version":[{"id":156348,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156343\/revisions\/156348"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156347"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}