{"id":200,"date":"2022-04-13T08:42:00","date_gmt":"2022-04-13T08:42:00","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=200"},"modified":"2025-12-04T12:10:51","modified_gmt":"2025-12-04T12:10:51","slug":"l-4-area-of-sectors","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/l-4-area-of-sectors\/","title":{"rendered":"L.4 Area of sectors"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Area of sectors<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd35 <strong>What is a Sector?<\/strong><\/h3>\n\n\n\n<p>A <strong>sector<\/strong> is a <strong>part of a circle<\/strong> that looks like a <strong>slice of pizza<\/strong> \ud83c\udf55 or a <strong>piece of pie<\/strong> \ud83e\udd67.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd36 <strong>Formula for Area of a Sector<\/strong><\/h3>\n\n\n\n<p>If a circle has <strong>radius r<\/strong> and the central angle is <strong>\u03b8 (in degrees)<\/strong>:<\/p>\n\n\n\n<p>\ud83d\udc49 <strong>Area of a sector = (\u03b8 \/ 360\u00b0) \u00d7 \u03c0r\u00b2<\/strong><\/p>\n\n\n\n<p>\ud83d\udfe3 <em>This formula tells us what fraction of the circle the sector represents.<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe9 <strong>When Angle is in Radians<\/strong><\/h3>\n\n\n\n<p>If angle is <strong>\u03b8 radians<\/strong>:<\/p>\n\n\n\n<p>\ud83d\udc49 <strong>Area = (1\/2) \u00d7 r\u00b2 \u00d7 \u03b8<\/strong><\/p>\n\n\n\n<p>\ud83d\udccf Radians are often used in higher classes, but good to know!<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe0 <strong>Understanding the Formula<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Full circle = <strong>360\u00b0<\/strong><\/li>\n\n\n\n<li>Sector = <strong>part of the circle<\/strong><br>So multiply <strong>fraction of circle<\/strong> \u00d7 <strong>area of full circle<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udc9b <strong>Important Terms<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Radius (r)<\/strong> \u279d distance from center to edge of circle<\/li>\n\n\n\n<li><strong>Central Angle (\u03b8)<\/strong> \u279d angle that opens the sector<\/li>\n\n\n\n<li><strong>\u03c0 (pi)<\/strong> \u279d approximately <strong>3.14<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe3 <strong>Area Depends On:<\/strong><\/h3>\n\n\n\n<p>\u2714 Size of angle (\u03b8) \u279d <strong>Bigger angle = bigger sector<\/strong><br>\u2714 Size of radius (r) \u279d <strong>Larger circle = larger sector<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udc99 <strong>Real-Life Examples of Sectors<\/strong><\/h3>\n\n\n\n<p>\ud83c\udf55 Pizza slices<br>\ud83d\udd57 Clock face sections<br>\ud83c\udfa1 Ferris wheel sections<br>\u2699 Machine gears<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\udde0 <strong>Sample Quick Example<\/strong><\/h3>\n\n\n\n<p>Find the area of a sector with<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>r = 7 cm<\/li>\n\n\n\n<li>\u03b8 = 60\u00b0<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 Area = (60\/360) \u00d7 \u03c0 \u00d7 7\u00b2<br>\ud83d\udc49 Area = (1\/6) \u00d7 \u03c0 \u00d7 49<br>\ud83d\udc49 Area = <strong>(49\u03c0 \/ 6) cm\u00b2<\/strong> \ud83c\udf89<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udf08 <strong>Tips for Solving Problems<\/strong><\/h3>\n\n\n\n<p>\u2b50 Convert angle to degrees or radians correctly<br>\u2b50 Always write formula first<br>\u2b50 Square the radius carefully<br>\u2b50 Simplify fractions before multiplying for ease<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f1cfcf\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-7902f4c11d9069dc8c1f14f591abf824\" style=\"color:#b00012\"><strong>The&nbsp;radius of a circle is&nbsp;10&nbsp;centimetres. What is the area of a sector bounded by a&nbsp;180\u00b0&nbsp;arc?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-11.png\" alt=\"\" class=\"wp-image-11755\" style=\"width:272px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give&nbsp;the exact answer in simplest&nbsp;form.<\/p>\n\n\n\n<p>___________ square&nbsp;centimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;sector&#8217;s area depends on the arc&#8217;s measure and the circle&#8217;s area. You already know that the arc&#8217;s measure is&nbsp;180\u00b0,&nbsp;so find the circle&#8217;s&nbsp;area.<\/p>\n\n\n\n<p>First,&nbsp;find the area of the&nbsp;circle.<\/p>\n\n\n\n<p>A = \ud835\udf0b r<sup>2<\/sup><\/p>\n\n\n\n<p>    =  \ud835\udf0b  10<sup>2<\/sup>    Plug&nbsp;in&nbsp;r=10<\/p>\n\n\n\n<p>     = 100 \ud835\udf0b     Square<\/p>\n\n\n\n<p>The&nbsp;area of the circle is&nbsp;100\u200b\ud835\udf0b  square&nbsp;centimetres.<\/p>\n\n\n\n<p>Now,&nbsp;find the area of the&nbsp;sector.<\/p>\n\n\n\n<p>K = A . m\/360<\/p>\n\n\n\n<p>    = 100 \ud835\udf0b  180 \/ 360     Plug&nbsp;in&nbsp;A=100\u200b\ud835\udf0b&nbsp;and&nbsp;m=180<\/p>\n\n\n\n<p>     = 50  \ud835\udf0b    Multiply&nbsp;and&nbsp;simplify<\/p>\n\n\n\n<p>The&nbsp;area of the sector is&nbsp; 50\u200b\ud835\udf0b&nbsp;square&nbsp;centimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#ccf7cc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-07caece7e51afb157b31a8bb33048a50\" style=\"color:#b00012\"><strong>The&nbsp;radius of a circle is&nbsp;8&nbsp;kilometres. What is the area of a sector bounded by a&nbsp;45\u00b0&nbsp;arc?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-12.png\" alt=\"\" class=\"wp-image-11764\" style=\"width:330px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give&nbsp;the exact answer in simplest&nbsp;form.<\/p>\n\n\n\n<p>_________ square&nbsp;kilometres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;sector&#8217;s area depends on the arc&#8217;s measure and the circle&#8217;s area. You already know that the arc&#8217;s measure is&nbsp;45\u00b0,&nbsp;so find the circle&#8217;s&nbsp;area.<\/p>\n\n\n\n<p>First,&nbsp;find the area of the&nbsp;circle.<\/p>\n\n\n\n<p>A = \ud835\udf0b r<sup>2<\/sup><\/p>\n\n\n\n<p>    =  \ud835\udf0b  8<sup>2<\/sup>    Plug&nbsp;in&nbsp;r=8<\/p>\n\n\n\n<p>     = 64 \ud835\udf0b     Square<\/p>\n\n\n\n<p>The&nbsp;area of the circle is&nbsp;64\u200b\ud835\udf0b square&nbsp;kilometres.<\/p>\n\n\n\n<p>Now,&nbsp;find the area of the&nbsp;sector.<\/p>\n\n\n\n<p>K = A . m\/360<\/p>\n\n\n\n<p>    = 64 \ud835\udf0b  45 \/ 360     Plug&nbsp;in&nbsp;A=64\u200b\ud835\udf0b&nbsp;and&nbsp;m=45<\/p>\n\n\n\n<p>     = 8  \ud835\udf0b    Multiply&nbsp;and&nbsp;simplify<\/p>\n\n\n\n<p>The&nbsp;area of the sector is&nbsp; 8\u200b\ud835\udf0b&nbsp;square&nbsp;kilometres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a7c2e3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-ea04a8e86ed2974e91862032d3f5bcb6\" style=\"color:#b00012\"><strong>The&nbsp;radius of a circle is&nbsp;6&nbsp;centimetres. What is the area of a sector bounded by a&nbsp;90\u00b0&nbsp;arc?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-13.png\" alt=\"\" class=\"wp-image-11780\" style=\"width:288px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give&nbsp;the exact answer in simplest&nbsp;form.<\/p>\n\n\n\n<p>___________ square&nbsp;centimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;sector&#8217;s area depends on the arc&#8217;s measure and the circle&#8217;s area. You already know that the arc&#8217;s measure is&nbsp;90\u00b0,&nbsp;so find the circle&#8217;s&nbsp;area.<\/p>\n\n\n\n<p>First,&nbsp;find the area of the&nbsp;circle.<\/p>\n\n\n\n<p>A = \ud835\udf0b r<sup>2<\/sup><\/p>\n\n\n\n<p>    =  \ud835\udf0b  6<sup>2<\/sup>    Plug&nbsp;in&nbsp;r=6<\/p>\n\n\n\n<p>     = 36 \ud835\udf0b     Square<\/p>\n\n\n\n<p>The&nbsp;area of the circle is&nbsp;36\u200b\ud835\udf0b  square&nbsp;centimetres.<\/p>\n\n\n\n<p>Now,&nbsp;find the area of the&nbsp;sector.<\/p>\n\n\n\n<p>K = A . m\/360<\/p>\n\n\n\n<p>    = 36 \ud835\udf0b  90 \/ 360     Plug&nbsp;in&nbsp;A=36\u200b \ud835\udf0b&nbsp;and&nbsp;m=90<\/p>\n\n\n\n<p>     = 9  \ud835\udf0b    Multiply&nbsp;and&nbsp;simplify<\/p>\n\n\n\n<p>The&nbsp;area of the sector is&nbsp; 9\u200b\ud835\udf0b&nbsp;square&nbsp;centimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<\/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\/88990\/009\/358\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69.png\" alt=\"\" class=\"wp-image-7892\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69-150x150.png 150w\" 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\/88987\/577\/534\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-78.png\" alt=\"\" class=\"wp-image-7893\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-78.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-78-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-78-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Area of sectors Key Notes : \ud83d\udd35 What is a Sector? A sector is a part of a circle that looks like a slice of pizza \ud83c\udf55 or a piece of pie \ud83e\udd67. \ud83d\udd36 Formula for Area of a Sector If a circle has radius r and the central angle is \u03b8 (in degrees): \ud83d\udc49<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/l-4-area-of-sectors\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.4 Area of sectors&#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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-200","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=200"}],"version-history":[{"count":18,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/200\/revisions"}],"predecessor-version":[{"id":18285,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/200\/revisions\/18285"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}