{"id":639426,"date":"2023-06-26T06:16:59","date_gmt":"2023-06-26T00:46:59","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-conical-cap-if-the-height-and-diameter-of-the-cylindrical-part-are-21-cm-and-40-cm-respectively-and-height-of-th\/"},"modified":"2025-06-26T12:44:34","modified_gmt":"2025-06-26T07:14:34","slug":"a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-conical-cap-if-the-height-and-diameter-of-the-cylindrical-part-are-21-cm-and-40-cm-respectively-and-height-of-th","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/","title":{"rendered":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy.","custom_permalink":"question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/"},"categories":[],"acf":{"question":"

A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are <\/span>21<\/mn> <\/mi><\/math>cm and <\/span>\r\n\r\n \r\n \r\n 40<\/m:mn> <\/m:mo>cm<\/m:mtext><\/m:mrow>\r\n <\/m:semantics><\/math>  respectively, and height of the cone is <\/span>\r\n\r\n \r\n \r\n 15<\/m:mn> <\/m:mo>cm<\/m:mtext><\/m:mrow>\r\n <\/m:semantics><\/math> , find the total surface area of the toy.<\/span><\/p>

<\/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":" 6453.7<\/m:mn>c<\/m:mi> m<\/m:mi> 2<\/m:mn> <\/m:msup> <\/m:mrow> <\/m:semantics><\/math> ","correct":false},{"option":"5466<\/mn>.<\/mo>37<\/mn> c<\/mi>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>","correct":true},{"option":" 8463.7<\/m:mn>c<\/m:mi> m<\/m:mi> 2<\/m:mn> <\/m:msup> <\/m:mrow> <\/m:semantics><\/math> ","correct":false},{"option":" 4463.6<\/m:mn>c<\/m:mi> m<\/m:mi> 2<\/m:mn> <\/m:msup> <\/m:mrow> <\/m:semantics><\/math>  <\/span>","correct":false}],"solution":"It is given that a toy is in the shape of a solid cylinder surmounted by a conical cap. The<\/span>  <\/span>height and diameter of the cylindrical part are <\/span>21<\/mn> <\/mi>cm<\/mi><\/math> and <\/span>40<\/mn> cm<\/mi><\/math> respectively. The height of the cone is <\/span>15<\/mn> cm<\/mi><\/math>.<\/span>
We have to find the required slant height. <\/span>
Let R and H be the radius and height of the conical top respectively. <\/span>
Suppose the given terms r and h be the radius and height of the cylindrical part.<\/span>
As we know the Slant height of the cone, <\/span>
l<\/mi>=<\/mo>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>+<\/mo>H<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/mrow><\/msqrt><\/math>
\u21d2<\/mo>l<\/mi>=<\/mo>(<\/mo>20<\/mn>)<\/mo><\/mrow>2<\/mn><\/mrow><\/msup>+<\/mo>(<\/mo>15<\/mn>)<\/mo><\/mrow>2<\/mn><\/mrow><\/msup><\/mrow><\/msqrt><\/math>
\u21d2<\/mo>l<\/mi>=<\/mo>400<\/mn>+<\/mo>225<\/mn><\/mrow><\/msqrt><\/math>
\u21d2<\/mo>l<\/mi>=<\/mo>625<\/mn><\/mrow><\/msqrt><\/math>
\u21d2<\/mo>l<\/mi>=<\/mo>25<\/mn> cm<\/mi><\/math>
Total surface of the toy = Curved surface area of cone + Curved surface area of cylinder + Area of base.<\/span>
We know that,<\/span>
Curved surface area of cone<\/mi>=<\/mo>\u03c0Rl<\/mi><\/math>
Curved surface area of cylinder<\/mi>=<\/mo>2<\/mn>\u03c0rh<\/mi><\/math>
Area of base<\/mi>=<\/mo>\u03c0<\/mi>r<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>
Therefore,<\/span>
Total surface of the toy<\/mi>=<\/mo>\u03c0Rl<\/mi>+<\/mo>2<\/mn>\u03c0rh<\/mi>+<\/mo>\u03c0<\/mi>r<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>
Substituing the values,<\/span>
\u21d2<\/mo>Total surface of the toy<\/mi>=<\/mo>\u03c0<\/mi>(<\/mo>20<\/mn>\u00d7<\/mo>25<\/mn>)<\/mo>+<\/mo>2<\/mn>\u03c0<\/mi>(<\/mo>20<\/mn>\u00d7<\/mo>21<\/mn>)<\/mo>+<\/mo>\u03c0<\/mi>(<\/mo>20<\/mn>)<\/mo><\/mrow>2<\/mn><\/mrow><\/msup><\/math>
\u21d2<\/mo>Total surface of the toy<\/mi>=<\/mo>\u03c0<\/mi>(<\/mo>500<\/mn>)<\/mo>+<\/mo>2<\/mn>\u03c0<\/mi>(<\/mo>420<\/mn>)<\/mo>+<\/mo>\u03c0<\/mi>(<\/mo>400<\/mn>)<\/mo><\/math>
\u21d2<\/mo>Total surface of the toy<\/mi>=<\/mo>1740<\/mn>\u03c0<\/mi><\/math>
\u21d2<\/mo>Total surface of the toy<\/mi>=<\/mo>1740<\/mn>\u00d7<\/mo>22<\/mn><\/mrow>7<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>Total surface of the toy<\/mi>=<\/mo>5466<\/mn>.<\/mo>37<\/mn> c<\/mi>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>
The total surface area of the toy is <\/span>5466<\/mn>.<\/mo>37<\/mn> c<\/mi>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>.<\/span>
Hence, option 2 is the correct answer.<\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nA toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy.\" \/>\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\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/\" \/>\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=\"2025-06-26T07:14:34+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":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy. - Infinity Learn by Sri Chaitanya","description":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy.","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\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/","og_locale":"en_US","og_type":"article","og_title":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy. - Infinity Learn by Sri Chaitanya","og_description":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy.","og_url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_modified_time":"2025-06-26T07:14:34+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\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/","name":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy. - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2023-06-26T00:46:59+00:00","dateModified":"2025-06-26T07:14:34+00:00","description":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-toy-is-in-the-shape-of-a-solid-cylinder-surmounted-by-a-co\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21\u00a0cm and 40\u00a0cm \u00a0 respectively, and height of the cone is 15\u00a0cm \u00a0, find the total surface area of the toy."}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/639426"}],"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=639426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=639426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}