{"id":455,"date":"2022-04-12T10:38:00","date_gmt":"2022-04-12T10:38:00","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=455"},"modified":"2025-11-10T08:49:27","modified_gmt":"2025-11-10T08:49:27","slug":"w-8-quarter-circles-calculate-area-perimeter-and-radius","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/w-8-quarter-circles-calculate-area-perimeter-and-radius\/","title":{"rendered":"W.8 Quarter circles: calculate area, perimeter and radius"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"> Quarter circles: calculate area, perimeter and radius<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG3JYe6Nks\/gVx7TlzVSyrs4VRlerrLVw\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3JYe6Nks&#x2F;gVx7TlzVSyrs4VRlerrLVw&#x2F;watch?utm_content=DAG3JYe6Nks&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>What is a Quarter Circle?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>quarter circle<\/strong> is <strong>one-fourth of a full circle<\/strong>.<\/p>\n\n\n\n<p>It looks like a \u201cslice\u201d of a circle, formed when a circle is divided into <strong>4 equal parts<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Key Formulas<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>(a) Area of a Quarter Circle<\/strong><\/h3>\n\n\n\n<p>A=1\/4\u00d7\u03c0r<sup>2<\/sup><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>(b) Perimeter of a Quarter Circle<\/strong><\/h3>\n\n\n\n<p>The perimeter consists of:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>One arc length<\/strong> (\u00bc of the circumference),<\/li>\n\n\n\n<li><strong>Two radii<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>P=1\/4\u00d72\u03c0r+2r<\/p>\n\n\n\n<p>P=1\/2\u200b\u03c0r+2r<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">(c) <strong>Radius from Area<\/strong><\/h3>\n\n\n\n<p>If area of a quarter circle is given: r=\u221a4A\/\u03c0<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong>Examples<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 1: Area<\/strong><\/h3>\n\n\n\n<p>Find the area of a quarter circle of radius 14 cm.  <\/p>\n\n\n\n<p>A=1\/4\u03c0r<sup>2<\/sup>=1\/4\u00d722\/7\u00d714\u00d714=154\u2009cm<sup>2<\/sup><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 2: Perimeter<\/strong><\/h3>\n\n\n\n<p>Find the perimeter of a quarter circle of radius 7 cm. <\/p>\n\n\n\n<p>P=1\/2\u03c0r+2r=1\/2\u00d722\/7\u00d77+14<\/p>\n\n\n\n<p>P=11+14=25\u2009cm<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>Example 3: Radius from Area<\/strong><\/h3>\n\n\n\n<p>The area of a quarter circle is 19.625 cm\u00b2. Find its radius (use \u03c0=3.14).  <\/p>\n\n\n\n<p>A=1\/4\u03c0r2\u2005\u200a\u27f9\u2005\u200ar2=4A\/\u03c0<\/p>\n\n\n\n<p>r<sup>2<\/sup>=4\u00d719.625\/3.14=25\u2005\u200a\u27f9\u2005\u200ar=5\u2009cm<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong><strong>Important Points<\/strong><\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>quarter circle = 90\u00b0 sector<\/strong> of a circle.<\/p>\n\n\n\n<p>Always add <strong>2 radii<\/strong> when finding the perimeter.<\/p>\n\n\n\n<p>Units:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Area \u2192 cm\u00b2, m\u00b2, etc.<\/li>\n\n\n\n<li>Perimeter \u2192 cm, m, etc.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong><strong><strong>Practice Questions<\/strong><\/strong><\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find the area of a quarter circle with radius 21 cm.<\/li>\n\n\n\n<li>Find the perimeter of a quarter circle with radius 14 cm.<\/li>\n\n\n\n<li>A quarter circle has area 77 cm\u00b2. Find its radius.<\/li>\n\n\n\n<li>A wire is bent into the shape of a quarter circle of radius 28 cm. Find the length of the wire.<\/li>\n\n\n\n<li>A quarter circular garden has a radius of 10 m. Find its area and perimeter.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-huge-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#f2ade5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u25b6\ufe0f <strong>The&nbsp;radius of a quarter circle is&nbsp;5&nbsp;metres.&nbsp;What&nbsp;is the quarter circle&#8217;s&nbsp;perimeter?<\/strong><\/p>\n\n\n\n<p>Use&nbsp;3.14 for&nbsp;\u200b\ud835\udf0b.&nbsp;<\/p>\n\n\n\n<p>________ metres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;radius is&nbsp;5&nbsp;metres. Replace&nbsp;r&nbsp;by&nbsp;5&nbsp;in the&nbsp;formula.<\/p>\n\n\n\n<p>p = 2\u200b\ud835\udf0br \/ 4 + 2r<\/p>\n\n\n\n<p>\u2248 2.3 . 14.5 \/ 4 + 2.5<\/p>\n\n\n\n<p>\u2248 31 . 4 \/ 4 + 10<\/p>\n\n\n\n<p>\u2248 7.85+10<\/p>\n\n\n\n<p>\u2248 17 . 85<\/p>\n\n\n\n<p>The perimeter is about 17.85 metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#96fbb9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u25b6\ufe0f <strong>The&nbsp;perimeter of a quarter circle is&nbsp;7.14&nbsp;millimetres. What is the quarter circle&#8217;s&nbsp;radius?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15.png\" alt=\"\" class=\"wp-image-5286\" style=\"aspect-ratio:1;width:406px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Use&nbsp;3.14 for&nbsp;\u200b\ud835\udf0b.&nbsp;<\/p>\n\n\n\n<p>_____ millimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;perimeter is&nbsp;7.14&nbsp;millimetres. Replace&nbsp;P&nbsp;by&nbsp;7.14&nbsp;in the&nbsp;formula.<\/p>\n\n\n\n<p>p = 2\u200b\ud835\udf0br \/ 4 + 2r<\/p>\n\n\n\n<p>7.14 \u2248 2.3 . 14r \/ 4 + 2r<\/p>\n\n\n\n<p>7.14 \u2248 6.28r \/ 4 + 2r<\/p>\n\n\n\n<p>7.14 \u2248 1.57r + 2r<\/p>\n\n\n\n<p>7.14 \u2248 3.57r<\/p>\n\n\n\n<p>7.14 \/ 3.57 \u2248 r<\/p>\n\n\n\n<p>2 \u2248 r<\/p>\n\n\n\n<p>The&nbsp;radius is about&nbsp;2&nbsp;millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#f7b0e5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u25b6\ufe0f <strong>The&nbsp;radius of a quarter circle is&nbsp;4&nbsp;millimetres.&nbsp;What&nbsp;is the quarter circle&#8217;s&nbsp;perimeter?<\/strong><\/p>\n\n\n\n<p>Use&nbsp;3.14 for&nbsp;\u200b\ud835\udf0b.&nbsp;<\/p>\n\n\n\n<p>______ millimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;radius is&nbsp;4&nbsp;millimetres. Replace&nbsp;r&nbsp;by&nbsp;4&nbsp;in the&nbsp;formula.<\/p>\n\n\n\n<p>p = 2\u200b\ud835\udf0br \/ 4 + 2r<\/p>\n\n\n\n<p>\u2248 2.3 . 14.4 \/ 4 + 2.4<\/p>\n\n\n\n<p>\u2248 25 . 12 \/ 4 + 8<\/p>\n\n\n\n<p>\u2248 6.28 + 8<\/p>\n\n\n\n<p>\u2248 14.28<\/p>\n\n\n\n<p>The perimeter is about 14.28 millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/101663\/864\/686\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-132.png\" alt=\"\" class=\"wp-image-6893\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-132.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-132-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-132-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-132-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/101664\/673\/775\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-134.png\" alt=\"\" class=\"wp-image-6894\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-134.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-134-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-134-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-134-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Quarter circles: calculate area, perimeter and radius Design by Delta publications Key Notes : What is a Quarter Circle? A quarter circle is one-fourth of a full circle. It looks like a \u201cslice\u201d of a circle, formed when a circle is divided into 4 equal parts. Key Formulas (a) Area of a Quarter Circle A=1\/4\u00d7\u03c0r2<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/w-8-quarter-circles-calculate-area-perimeter-and-radius\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.8 Quarter circles: calculate area, perimeter and radius&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-455","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/455","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=455"}],"version-history":[{"count":23,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/455\/revisions"}],"predecessor-version":[{"id":17566,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/455\/revisions\/17566"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}