{"id":8914,"date":"2021-12-07T20:30:14","date_gmt":"2021-12-07T15:00:14","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8914"},"modified":"2021-12-09T00:12:50","modified_gmt":"2021-12-08T18:42:50","slug":"formula-for-length-of-arc-of-circle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/","title":{"rendered":"Formula for Length of Arc of Circle with Examples"},"content":{"rendered":"

Here you will learn what is the formula for length of arc of circle with examples based on it.<\/p>\n

Let’s begin –<\/p>\n

What is an Arc ?<\/h2>\n

Arc is a piece of circle. In the figure AB is an arc.<\/p>\n

The area OAB in the figure is called sector of the circle.<\/p>\n

Formula for Length of Arc of Circle<\/h2>\n

Let an arc AB make an angle \\(\\theta\\) < 180 at the centre of circle of radius r.\"length<\/p>\n

Then,<\/p>\n

\n

Length of the arc = \\(2\\pi r \\theta\\over 360\\)<\/p>\n

i.e. \\(l\\) =  \\(\\pi r \\theta\\over 180\\)<\/p>\n<\/blockquote>\n

Also Read<\/strong> : Area of a Ring \u2013 Formula and Examples<\/a><\/p>\n

Example<\/strong><\/span> : A sector is cut from a circle of radius 42 cm. The angle of the sector is 120. Find the length of its arc.<\/p>\n

Solution<\/strong><\/span> : Here r = 42 cm and \\(\\theta\\) = 120<\/p>\n

Length of arc of sector of angle \\(\\theta\\) and radius r = \\(l\\) = \\(\\pi r \\theta\\over 180\\)<\/p>\n

\\(\\implies\\)   \\(l\\) = \\(120\\over 180\\) \\(\\times\\) \\(22\\over 7\\) \\(\\times\\) 42 = 88 cm<\/p>\n

Hence, length of arc is 88 cm.<\/p>\n

Example<\/strong><\/span> : A pendulum swings through an angle 60 and describes an arc 8.8 cm in length. Find the length of the pendulum.<\/p>\n

Solution<\/strong><\/span> : Here, length of arc (\\(l\\)) = 8.8 cm and \\(\\theta\\) = 60<\/p>\n

Length of arc of sector of angle \\(\\theta\\) and radius r = \\(l\\) = \\(\\pi r \\theta\\over 180\\)<\/p>\n

\\(\\implies\\)   8.8 = \\(60\\over 180\\) \\(\\times\\) \\(22\\over 7\\) \\(\\times\\) r<\/p>\n

\\(\\implies\\)  r = \\(8.8 \\times 180 \\times 7\\over 60 \\times 22\\)<\/p>\n

\\(\\implies\\) r = \\(4.4 \\times 3 \\times 7\\over 11\\)  cm = 8.4 cm<\/p>\n

Hence, length of pendulum is 88 cm.<\/p>\n\n\n

\n
Next – Sector of a Circle Area and Perimeter<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Area of a Ring – Formula and Examples<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the formula for length of arc of circle with examples based on it. Let’s begin – What is an Arc ? Arc is a piece of circle. In the figure AB is an arc. The area OAB in the figure is called sector of the circle. Formula for Length …<\/p>\n

Formula for Length of Arc of Circle 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":[711,712,709,710],"yoast_head":"\nFormula for Length of Arc of Circle with Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula for length of arc of circle with 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-length-of-arc-of-circle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Length of Arc of Circle with Examples\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn what is the formula for length of arc of circle with examples based on it.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-12-07T15:00:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-12-08T18:42:50+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2021\/12\/lengthofarc-e1638888191464-279x300.png\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Formula for Length of Arc of Circle with Examples\",\"datePublished\":\"2021-12-07T15:00:14+00:00\",\"dateModified\":\"2021-12-08T18:42:50+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/\"},\"wordCount\":263,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"how to find arc length\",\"how to find the length of arc\",\"length of arc formula\",\"length of minor arc formula\"],\"articleSection\":[\"Surface Area & Volumes\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/\",\"url\":\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/\",\"name\":\"Formula for Length of Arc of Circle with Examples\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-12-07T15:00:14+00:00\",\"dateModified\":\"2021-12-08T18:42:50+00:00\",\"description\":\"In this post you will learn what is the formula for length of arc of circle with examples based on it.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Formula for Length of Arc of Circle with Examples\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Formula for Length of Arc of Circle with Examples","description":"In this post you will learn what is the formula for length of arc of circle with examples based on it.","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:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/","og_locale":"en_US","og_type":"article","og_title":"Formula for Length of Arc of Circle with Examples","og_description":"In this post you will learn what is the formula for length of arc of circle with examples based on it.","og_url":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/","og_site_name":"Mathemerize","article_published_time":"2021-12-07T15:00:14+00:00","article_modified_time":"2021-12-08T18:42:50+00:00","og_image":[{"url":"https:\/\/mathemerize.com\/wp-content\/uploads\/2021\/12\/lengthofarc-e1638888191464-279x300.png"}],"author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Formula for Length of Arc of Circle with Examples","datePublished":"2021-12-07T15:00:14+00:00","dateModified":"2021-12-08T18:42:50+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/"},"wordCount":263,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"keywords":["how to find arc length","how to find the length of arc","length of arc formula","length of minor arc formula"],"articleSection":["Surface Area & Volumes"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/","url":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/","name":"Formula for Length of Arc of Circle with Examples","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-12-07T15:00:14+00:00","dateModified":"2021-12-08T18:42:50+00:00","description":"In this post you will learn what is the formula for length of arc of circle with examples based on it.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/formula-for-length-of-arc-of-circle\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Formula for Length of Arc of Circle with Examples"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/8914"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=8914"}],"version-history":[{"count":6,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/8914\/revisions"}],"predecessor-version":[{"id":8936,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/8914\/revisions\/8936"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=8914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=8914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=8914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}