{"id":640184,"date":"2023-06-26T07:52:52","date_gmt":"2023-06-26T02:22:52","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-heights-are-in-the-ratio-3-5-what-is-the-ratio-of-their-curved-surface-area\/"},"modified":"2025-06-26T17:40:03","modified_gmt":"2025-06-26T12:10:03","slug":"the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-heights-are-in-the-ratio-3-5-what-is-the-ratio-of-their-curved-surface-area","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/","title":{"rendered":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?","custom_permalink":"question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:0pt; line-height:normal\"><span>The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?<\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><spanstyle=\"-aw-import:ignore\"><p><\/p><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><spanstyle=\"-aw-import:ignore\"><p><\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":[{"option":"3: 7","correct":true},{"option":"7: 3","correct":false},{"option":"5: 7","correct":false},{"option":"3: 5<span>&nbsp;<\/span>","correct":false}],"solution":"<span>Given,<\/span><br><span>Two cylinders whose radii are in ratio 5:7 and height in the ratio 3:5.<\/span><br><span>Let the radius of the first cylinder be <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:msub>\r\n    <m:mi>r<\/m:mi>\r\n    <m:mn>1<\/m:mn>\r\n   <\/m:msub>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>, height of first cylinder be <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:msub>\r\n    <m:mi>h<\/m:mi>\r\n    <m:mn>1<\/m:mn>\r\n   <\/m:msub>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>, the radius of the second cylinder be <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:msub>\r\n    <m:mi>r<\/m:mi>\r\n    <m:mn>2<\/m:mn>\r\n   <\/m:msub>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span> and height of second cylinder be <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:msub>\r\n    <m:mi>h<\/m:mi>\r\n    <m:mn>2<\/m:mn>\r\n   <\/m:msub>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>.<\/span><br><span>According to question, <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mfrac>\r\n    <m:mrow>\r\n     <m:msub>\r\n      <m:mi>r<\/m:mi>\r\n      <m:mn>1<\/m:mn>\r\n     <\/m:msub>\r\n     <\/m:mrow>\r\n    <m:mrow>\r\n     <m:msub>\r\n      <m:mi>r<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msub>\r\n     <\/m:mrow>\r\n   <\/m:mfrac>\r\n   <m:mo>=<\/m:mo><m:mfrac>\r\n    <m:mn>5<\/m:mn>\r\n    <m:mn>7<\/m:mn>\r\n   <\/m:mfrac>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span> and <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mfrac>\r\n    <m:mrow>\r\n     <m:msub>\r\n      <m:mi>h<\/m:mi>\r\n      <m:mn>1<\/m:mn>\r\n     <\/m:msub>\r\n     <\/m:mrow>\r\n    <m:mrow>\r\n     <m:msub>\r\n      <m:mi>h<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msub>\r\n     <\/m:mrow>\r\n   <\/m:mfrac>\r\n   <m:mo>=<\/m:mo><m:mfrac>\r\n    <m:mn>3<\/m:mn>\r\n    <m:mn>5<\/m:mn>\r\n   <\/m:mfrac>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<br><span>The curved surface area of first cylinder is <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n    <m:mi>A<\/m:mi>\r\n    <m:mn>1<\/m:mn>\r\n   <\/m:msub>\r\n   <m:mo>=<\/m:mo><m:mn>2<\/m:mn><m:mi>\u03c0<\/m:mi><m:msub>\r\n    <m:mi>r<\/m:mi>\r\n    <m:mn>1<\/m:mn>\r\n   <\/m:msub>\r\n   <m:msub>\r\n    <m:mi>h<\/m:mi>\r\n    <m:mn>1<\/m:mn>\r\n   <\/m:msub>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>.<\/span><br><span>The curved surface area of second cylinder is <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n    <m:mi>A<\/m:mi>\r\n    <m:mn>2<\/m:mn>\r\n   <\/m:msub>\r\n   <m:mo>=<\/m:mo><m:mn>2<\/m:mn><m:mi>\u03c0<\/m:mi><m:msub>\r\n    <m:mi>r<\/m:mi>\r\n    <m:mn>2<\/m:mn>\r\n   <\/m:msub>\r\n   <m:msub>\r\n    <m:mi>h<\/m:mi>\r\n    <m:mn>2<\/m:mn>\r\n   <\/m:msub>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>.<\/span><br><span>The ratio of the curved surface areas is given by<\/span><br><span>&nbsp;<\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mfrac>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     <m:mo>=<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:mn>2<\/m:mn><m:mi>\u03c0<\/m:mi><m:msub>\r\n        <m:mi>r<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <m:msub>\r\n        <m:mi>h<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:mn>2<\/m:mn><m:mi>\u03c0<\/m:mi><m:msub>\r\n        <m:mi>r<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <m:msub>\r\n        <m:mi>h<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     <m:mo>=<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:msub>\r\n        <m:mi>r<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:msub>\r\n        <m:mi>r<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     <m:mo>\u00d7<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:msub>\r\n        <m:mi>h<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:msub>\r\n        <m:mi>h<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     <m:mo>=<\/m:mo><m:mfrac>\r\n      <m:mn>5<\/m:mn>\r\n      <m:mn>7<\/m:mn>\r\n     <\/m:mfrac>\r\n     <m:mo>\u00d7<\/m:mo><m:mfrac>\r\n      <m:mn>3<\/m:mn>\r\n      <m:mn>5<\/m:mn>\r\n     <\/m:mfrac>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>1<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:mi>C<\/m:mi><m:mi>S<\/m:mi><m:msub>\r\n        <m:mi>A<\/m:mi>\r\n        <m:mn>2<\/m:mn>\r\n       <\/m:msub>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     <m:mo>=<\/m:mo><m:mfrac>\r\n      <m:mn>3<\/m:mn>\r\n      <m:mn>7<\/m:mn>\r\n     <\/m:mfrac>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<span> <\/span><span>Therefore, the ratio of the curved surface of the cylinders is 3:7.<\/span><br><span>Hence, the correct option is 1.<\/span><br><span>&nbsp;<\/span>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area? - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area? - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-26T12:10:03+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area? - Infinity Learn by Sri Chaitanya","description":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/","og_locale":"en_US","og_type":"article","og_title":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area? - Infinity Learn by Sri Chaitanya","og_description":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?","og_url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_modified_time":"2025-06-26T12:10:03+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/","name":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area? - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2023-06-26T02:22:52+00:00","dateModified":"2025-06-26T12:10:03+00:00","description":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-radii-of-two-cylinders-are-in-the-ratio-5-7-and-their-h\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?"}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/640184"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=640184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=640184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}