{"id":8839,"date":"2021-12-05T18:34:18","date_gmt":"2021-12-05T13:04:18","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8839"},"modified":"2021-12-05T21:30:58","modified_gmt":"2021-12-05T16:00:58","slug":"formula-for-volume-of-cone","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-volume-of-cone\/","title":{"rendered":"Formula for Volume of Cone with Examples"},"content":{"rendered":"

Here you will learn what is the formula for volume of cone and examples based on it.<\/p>\n

Let’s begin –<\/p>\n

What is Cone ?<\/h2>\n

A cone is a solid which has a circle at its base and a slanting lateral surface that converges at the apex. Its dimensions are defined by the radius of the base (r), the height (h) and the slant height (l).<\/p>\n

Also Read : Surface Area of Cone \u2013 Formula & Examples<\/a><\/p>\n

Formula for Volume of Cone<\/h2>\n
\n

Volume of Cone = \\(1\\over 3\\) \\(\\pi r^2 h\\)<\/p>\n<\/blockquote>\n

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

Example<\/span><\/strong> :  The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.<\/span> <\/p>\n

Solution<\/span><\/strong> : Here h = 21 and \\(l\\) = 28<\/p>\n

We know that, \\(l^2\\) = \\(r^2\\) + \\(h^2\\)<\/span>. <\/span><\/p>\n

\\(\\implies\\) \\(r^2\\) = \\(l^2\\) – \\(h^2\\)<\/p>\n

\\(\\implies\\) r = \\(\\sqrt{ 28^2 – 21^2}\\) = \\(7\\sqrt{7}\\)<\/p>\n

So, Volume of the Cone = \\(1\\over 3\\) \\(\\pi r^2 h\\)<\/p>\n

= \\(1\\over 3\\) \\(\\pi \\times 343 \\times 21\\)<\/p>\n

= 7546 \\(cm^3\\)<\/p>\n

Example<\/span><\/strong> : In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath. What should be the height of the conical tent ? <\/p>\n

Solution<\/span><\/strong> : Let the height of the conical tent = h metre.<\/p>\n

Radius of the base of the cone = r meter.<\/p>\n

The tent has to accommodate 150 persons.<\/p>\n

The space required by each person on the ground = 4 \\(m^2\\)<\/p>\n

And the amount of air = 20 \\(m^3\\)<\/p>\n

\\(\\therefore\\)  Area of the base = 150 \\(\\times\\) 4 = 600 \\(m^2\\)<\/p>\n

\\(\\implies\\)   \\(\\pi r^2\\) = 600 \\(\\implies\\) r = 13.817 m<\/p>\n

Volume of the air required for 150 persons = 150 \\(\\times\\) 20 = 3000 \\(m^3\\)<\/p>\n

\\(\\implies\\)  \\(1\\over 3\\) \\(\\pi r^2 h\\) = 3000 \\(m^3\\)<\/p>\n

\\(\\implies\\) h = \\(3000 \\times 7 \\times 3\\over 22 \\times (13.817)^2\\) = 15 m<\/p>\n

Hence the height of the conical tent is 15 m.<\/p>\n\n\n

\n
Next – Formula for Surface Area of Sphere with Examples<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Surface Area of Cone \u2013 Formula & Examples<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the formula for volume of cone and examples based on it. Let’s begin – What is Cone ? A cone is a solid which has a circle at its base and a slanting lateral surface that converges at the apex. Its dimensions are defined by the radius of the …<\/p>\n

Formula for Volume of Cone with Examples<\/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":[692,693,695,694],"yoast_head":"\nFormula for Volume of Cone with Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula for volume of cone and examples based on it.\" \/>\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-volume-of-cone\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Volume of Cone with Examples - 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