{"id":198,"date":"2022-04-13T08:41:38","date_gmt":"2022-04-13T08:41:38","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=198"},"modified":"2025-12-04T12:05:57","modified_gmt":"2025-12-04T12:05:57","slug":"l-3-arc-measure-and-arc-length","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/l-3-arc-measure-and-arc-length\/","title":{"rendered":"L.3 Arc measure and arc length"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Arc measure and arc length<\/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 an Arc?<\/strong><\/h3>\n\n\n\n<p>An <strong>arc<\/strong> is a part of the circumference of a circle.<\/p>\n\n\n\n<p>It looks like a <strong>curved segment<\/strong> of the circle.<\/p>\n\n\n\n<p>Two types:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Minor Arc<\/strong> \u279d smaller than half the circle<\/li>\n\n\n\n<li><strong>Major Arc<\/strong> \u279d larger than half the circle<\/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\udfe2 <strong>Arc Measure (in degrees) \ud83c\udfaf<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Arc measure is the <strong>degree measure<\/strong> of the central angle that forms the arc.<\/li>\n\n\n\n<li>A full circle = <strong>360\u00b0<\/strong><\/li>\n\n\n\n<li>Minor arcs: measure &lt; 180\u00b0<\/li>\n\n\n\n<li>Major arcs: measure > 180\u00b0<\/li>\n\n\n\n<li>Example: If central angle = <strong>60\u00b0<\/strong>, then arc measure = <strong>60\u00b0<\/strong> \ud83c\udf89<\/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>Arc Length (actual distance) \ud83d\udccf<\/strong><\/h3>\n\n\n\n<p>Arc length tells <strong>how long the curved part is<\/strong> (in cm, m, etc.).<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2728 <strong>Formula for Arc Length:<\/strong><\/h3>\n\n\n\n<p>Arc\u00a0Length = \u03b8 \/ 360<sup>\u2218<\/sup> \u00d7 2\u03c0r<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03b8 = arc measure (in degrees)<\/li>\n\n\n\n<li>r = radius of the circle<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udcdd <strong>Example:<\/strong><br>If r = 7\u2009cm and \u03b8 = 90\u2218<\/p>\n\n\n\n<p><strong>Arc\u00a0Length = 90 \/ 360 \u00d7 2\u03c0(7) = 14\u03c0 = 3.5\u03c0\u00a0cm<\/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\udfe1 <strong>Relationship between Arc Measure &amp; Length<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Arc measure<\/strong> = tells \u201chow big the angle is\u201d (in \u00b0)<\/li>\n\n\n\n<li><strong>Arc length<\/strong> = tells \u201chow long the curved path is\u201d (in cm\/m)<\/li>\n\n\n\n<li>Bigger angle = <strong>longer arc<\/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\udd34 <strong>Special Case: Semicircle<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A semicircle = <strong>half the circle<\/strong><\/li>\n\n\n\n<li>Arc measure = <strong>180\u00b0<\/strong><\/li>\n\n\n\n<li>Arc length = <strong>\u00bd \u00d7 circumference<\/strong> = \u03c0r\\pi r\u03c0r<\/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\">\ud83c\udf1f <strong>Tips to Remember<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use <strong>degrees<\/strong> for arc measure.<\/li>\n\n\n\n<li>Use <strong>radius<\/strong> for arc length.<\/li>\n\n\n\n<li>Always check if angle is <strong>minor or major<\/strong>.<\/li>\n\n\n\n<li>For full circle: arc length = <strong>2\u03c0r<\/strong> \ud83c\udf89<\/li>\n<\/ul>\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:#d7f7fc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-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 has-link-color wp-elements-67ae0c6cd5ab8c878edac7f8b7b67b32\" style=\"color:#b00012\"><strong>\ud83d\udd14 The&nbsp;radius of a circle is&nbsp;3&nbsp;metres. What is the length of a&nbsp;90\u00b0&nbsp;arc?<\/strong><\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-8.png\" alt=\"\" class=\"wp-image-11720\" style=\"width:316px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give the exact answer in simplest form.<br>________ metres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;arc&#8217;s length depends on the arc&#8217;s measure and the circle&#8217;s circumference. You already know that the arc&#8217;s measure is&nbsp;90\u00b0,&nbsp;so find the circle&#8217;s&nbsp;circumference.<\/p>\n\n\n\n<p>First, find the circumference.<\/p>\n\n\n\n<p>C = 2\u200b\ud835\udf0br<\/p>\n\n\n\n<p>= 2\u200b\ud835\udf0b(3)                       Plug in r=3<\/p>\n\n\n\n<p>= 6\u200b\ud835\udf0b                        Multiply<\/p>\n\n\n\n<p>The circumference is 6\u200b\ud835\udf0b metres.<br>Now, find the length of the arc.<\/p>\n\n\n\n<p>\ud835\udcc1 = C . m \/ 360<\/p>\n\n\n\n<p>= 6\u200b\ud835\udf0b . 90 \/ 360                      Plug in C=6\u200b\ud835\udf0b and m=90<\/p>\n\n\n\n<p>= 3\u200b\ud835\udf0b \/ 2                             Multiply and simplify<\/p>\n\n\n\n<p>The length of the arc is 3\u200b\ud835\udf0b \/ 2  metres<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e4f4d9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-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 has-link-color wp-elements-771af1d042be3592af5bd813439cd8b6\" style=\"color:#b00012\"><strong>\ud83d\udd14 The&nbsp;radius of a circle is&nbsp;5&nbsp;kilometres. What is the length of a&nbsp;135\u00b0&nbsp;arc?<\/strong><\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-9.png\" alt=\"\" class=\"wp-image-11723\" style=\"width:311px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give the exact answer in simplest form.<br>________ kilometres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;arc&#8217;s length depends on the arc&#8217;s measure and the circle&#8217;s circumference. You already know that the arc&#8217;s measure is&nbsp;135\u00b0,&nbsp;so find the circle&#8217;s&nbsp;circumference.<\/p>\n\n\n\n<p>First, find the circumference.<\/p>\n\n\n\n<p>C = 2\u200b\ud835\udf0br<\/p>\n\n\n\n<p>= 2\u200b\ud835\udf0b(5)                              Plug in r=5<\/p>\n\n\n\n<p>= 10\u200b\ud835\udf0b                             Multiply<\/p>\n\n\n\n<p>The&nbsp;circumference is&nbsp;10\u200b\ud835\udf0b&nbsp;kilometres.<\/p>\n\n\n\n<p>Now,&nbsp;find the length of the&nbsp;arc.<\/p>\n\n\n\n<p>\ud835\udcc1=C . m \/ 360<\/p>\n\n\n\n<p>= 10\u200b\ud835\udf0b . 135 \/ 360                                         Plug in C=10\u200b\ud835\udf0b and m=135<\/p>\n\n\n\n<p>= 15\ud835\udf0b \/ 4                                                 Multiply and simplify<\/p>\n\n\n\n<p>The&nbsp;length of the arc is&nbsp;15\ud835\udf0b \/ 4 kilometres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f8dcfa\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-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 has-link-color wp-elements-ccd9af4da0b8372b798680824312d0a9\" style=\"color:#b00012\"><strong>\ud83d\udd14 The radius of a circle is 10 centimetres. What is the length of a 135\u00b0 arc?<\/strong><\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-10.png\" alt=\"\" class=\"wp-image-11729\" style=\"width:290px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give&nbsp;the exact answer in simplest&nbsp;form.&nbsp;<\/p>\n\n\n\n<p>________ centimetres<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;arc&#8217;s length depends on the arc&#8217;s measure and the circle&#8217;s circumference. You already know that the arc&#8217;s measure is&nbsp;135\u00b0,&nbsp;so find the circle&#8217;s&nbsp;circumference.<\/p>\n\n\n\n<p>First,&nbsp;find the&nbsp;circumference.<\/p>\n\n\n\n<p>C = 2\u200b\ud835\udf0br<\/p>\n\n\n\n<p>= 2\u200b\ud835\udf0b(10)                                                   Plug in r=10<\/p>\n\n\n\n<p>= 20\u200b\ud835\udf0b                                                    Multiply<\/p>\n\n\n\n<p>The&nbsp;circumference is&nbsp;20\u200b\ud835\udf0b&nbsp;centimetres.<\/p>\n\n\n\n<p>Now,&nbsp;find the length of the&nbsp;arc.<\/p>\n\n\n\n<p>\ud835\udcc1 = C . m \/ 360<\/p>\n\n\n\n<p>=<strong>20\u200b\ud835\udf0b<\/strong> . 135 \/ 360 Plug in C=20\u200b\ud835\udf0b and m=135<\/p>\n\n\n\n<p>= 15\u200b\ud835\udf0b \/ 2 Multiply&nbsp;and&nbsp;simplify<\/p>\n\n\n\n<p>The length of the arc is 15\u200b\ud835\udf0b \/ 2 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\/88994\/214\/347\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-70.png\" alt=\"\" class=\"wp-image-7896\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-70.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-70-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-70-150x150.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\/88996\/115\/732\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-79.png\" alt=\"\" class=\"wp-image-7897\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-79.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-79-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-79-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#06786a\"><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Arc measure and arc length Key Notes : \ud83d\udd35 What is an Arc? An arc is a part of the circumference of a circle. It looks like a curved segment of the circle. Two types: \ud83d\udfe2 Arc Measure (in degrees) \ud83c\udfaf \ud83d\udfe3 Arc Length (actual distance) \ud83d\udccf Arc length tells how long the curved part<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/l-3-arc-measure-and-arc-length\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.3 Arc measure and arc length&#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-198","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/198","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=198"}],"version-history":[{"count":15,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/198\/revisions"}],"predecessor-version":[{"id":18279,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/198\/revisions\/18279"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}