{"id":7692,"date":"2021-11-05T18:50:04","date_gmt":"2021-11-05T13:20:04","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7692"},"modified":"2022-01-16T17:10:59","modified_gmt":"2022-01-16T11:40:59","slug":"formula-for-surface-area-of-cylinder","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cylinder\/","title":{"rendered":"Formula for Surface Area of cylinder – Derivation and Example"},"content":{"rendered":"

Here you will learn formula for surface area of cylinder (total surface area and curved surface area) with examples.<\/p>\n

Let’s begin – <\/p>\n

Formula for Surface Area of cylinder<\/h2>\n

(a) Total Surface Area<\/h3>\n
\n

T.S.A = \\(2\\pi r(h + r)\\)<\/p>\n<\/blockquote>\n

(b) Curved Surface Area<\/h3>\n
\n

C.S.A = \\(2\\pi rh\\)<\/p>\n<\/blockquote>\n

Also Read<\/strong> : Formula for Volume of Cylinder \u2013 Definition & Examples<\/a><\/p>\n

Derivation<\/strong> :<\/h4>\n

Let take a rectangular sheet. The rectangular sheet when folded becomes a cylinder as shown in figure.<\/span>\"cylinder\"<\/p>\n

The area of the rectangular sheet gives the curved surface area of the cylinder. Note that the length of the sheet is equal to the circumference of the circular base of cylinder which is equal to 2<\/span>\u03c0<\/span>r<\/span>.<\/span><\/p>\n

So, the curved surface area of the cylinder = area of the rectangular sheet = \\length\\times breadth\\) <\/span>= 2<\/span>\u03c0<\/span>r <\/span>\u00d7 <\/span>h<\/span><\/p>\n

Therefore,the Curved Surface Area of Cylinder = \\(2\\pi rh\\)<\/strong><\/p>\n

In the case of a cylinder, unless stated otherwise, \u2018radius of a cylinder\u2019 means base radius of the cylinder.<\/span><\/p>\n

If top and the bottom of the cylinder are also to be covered, then we need two circles to do that, each of radius <\/span>r<\/span>, and thus having an <\/span>area <\/span>of \\(\\pi r^2\\).<\/span> giving us the total surface area of cylinder as \\(2\\pi <\/span>rh\\) <\/span>+ \\(2<\/span>\u03c0<\/span>r^2\\)<\/span> <\/span>= 2<\/span>\u03c0<\/span>r<\/span>(<\/span>r <\/span>+ <\/span>h<\/span>).<\/span><\/p>\n

So, the Total Surface Area of Cylinder = 2<\/span>\u03c0<\/span>r<\/span>(<\/span>r <\/span>+ <\/span>h<\/span>).<\/span><\/strong><\/p>\n

where <\/span>r  and h <\/span>is the radius of the base of cylinder and<\/span> height of cylinder respectively.<\/span><\/p>\n

Example<\/span><\/strong> : Nandini had to make cylindrical object. She wanted to use cover curved surface of object with chart paper. What is the area of chart paper required, if she wanted to make object of height 15 cm with a 3.5 cm radius?<\/span> <\/p>\n

Solution<\/span><\/strong> : Radius of the base of the cylindrical object (<\/span>r<\/span>) = 3.5 cm.<\/span><\/p>\n

Height of object (<\/span>h<\/span>) = 15 cm.<\/span><\/p>\n

Area of the chart paper required = curved surface area of the object<\/span><\/p>\n

= 2<\/span>\u03c0<\/span>rh = \\(2\\times {22\\over 7}\\times 3.5 \\times 15\\)<\/span><\/p>\n

= 330 \\(cm^2\\)<\/p>\n\n\n

\n
Next – Formula for Volume of Cylinder<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Formula for Volume of Cube<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn formula for surface area of cylinder (total surface area and curved surface area) with examples. Let’s begin –  Formula for Surface Area of cylinder (a) Total Surface Area T.S.A = \\(2\\pi r(h + r)\\) (b) Curved Surface Area C.S.A = \\(2\\pi rh\\) Also Read : Formula for Volume of Cylinder \u2013 …<\/p>\n

Formula for Surface Area of cylinder – Derivation and Example<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[63],"tags":[669,671,670],"yoast_head":"\nFormula for Surface Area of cylinder - Derivation and Example<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula for surface area of cylinder (total surface area and curved surface area) with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cylinder\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Surface Area of cylinder - 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