{"id":8899,"date":"2021-12-06T22:42:01","date_gmt":"2021-12-06T17:12:01","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8899"},"modified":"2021-12-07T20:43:03","modified_gmt":"2021-12-07T15:13:03","slug":"area-of-a-ring","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/area-of-a-ring\/","title":{"rendered":"Area of a Ring – Formula and Examples"},"content":{"rendered":"

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

Let’s begin –<\/p>\n

Area of a Ring<\/h2>\n

Let R and r be the outer and inner radii of a ring. \"circular<\/p>\n

\n

Then, area of a ring = \\(\\pi(R^2 – r^2)\\)<\/p>\n<\/blockquote>\n

Also Read : Area of a Circle and Semicircle \u2013 Formula & Examples<\/a><\/p>\n

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

We know that area of circle = \\(\\pi r^2\\)<\/p>\n

To calculate the area of ring (concentric circle), we subtract area of smaller circle from the area of bigger circle.<\/p>\n

So, Area of rings = Area of bigger circle\u00a0 – Area of inner circle<\/p>\n

= \\(\\pi R^2\\) – \\(\\pi r^2\\)<\/p>\n

= \\(\\pi(R^2 – r^2)\\)<\/p>\n

Hence, the area is \\(\\pi(R^2 – r^2)\\).<\/p>\n

Example<\/span><\/strong> : Find the area of the circular ring whose outer radius is 5 cm and inner radius is 4 cm.<\/p>\n

Solution<\/span><\/strong> : Here, R = 5 cm and r = 3 cm<\/p>\n

So, Area = \\(\\pi(R^2 – r^2)\\) = \\(3.14 \\times (25 -16)\\) = \\(3.14 \\times 9\\) = 28.26<\/p>\n

Example<\/span><\/strong> : The area enclosed between two concentric is 770 \\(cm^2\\). If radius of the outer circle is 21 cm, find the radius of the inner circle.<\/p>\n

Solution<\/span><\/strong> : Radius of outer circle = 21 cm<\/p>\n

Area enclosed between two concentric circles = 770 \\(cm^2\\)<\/p>\n

Let the radius of inner circle be r.<\/p>\n

Then, according to question<\/p>\n

\\(\\pi (21)^2\\) – \\(\\pi r^2\\) = 770<\/p>\n

\\(\\implies\\)\u00a0 \u00a0 \u00a0 \\(21^2\\) – \\(r^2\\) = \\(770 \\times 7\\over 22\\)<\/p>\n

\\(\\implies\\)\u00a0 \\(r^2\\) = 441 – \\(70 \\times 7\\over 2\\) = 441 – 245 = 196<\/p>\n

\\(\\implies\\)\u00a0 \u00a0r = \\(\\sqrt{196}\\) = 14 cm<\/p>\n

Hence, the radius of inner circle is 14 cm.<\/p>\n\n\n

\n
Next – Formula for Length of Arc of Circle<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Area of a Circle and Semicircle<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the formula for the area of circular ring and examples based on it. Let’s begin – Area of a Ring Let R and r be the outer and inner radii of a ring. Then, area of a ring = \\(\\pi(R^2 – r^2)\\) Also Read : Area of a Circle …<\/p>\n

Area of a Ring – Formula and 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":[707,708],"yoast_head":"\nArea of a Ring - Formula and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula for the area of circular ring 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\/area-of-a-ring\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Area of a Ring - 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