{"id":202,"date":"2022-04-13T08:42:16","date_gmt":"2022-04-13T08:42:16","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=202"},"modified":"2025-12-04T12:12:32","modified_gmt":"2025-12-04T12:12:32","slug":"l-5-circle-measurements-mixed-review","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/l-5-circle-measurements-mixed-review\/","title":{"rendered":"L.5 Circle measurements: mixed review"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Circle measurements: mixed review<\/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<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd35 <strong>Parts of a Circle<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Radius (r)<\/strong> \u279c Distance from center to any point on the circle.<\/li>\n\n\n\n<li><strong>Diameter (d)<\/strong> \u279c Twice the radius ( <strong>d = 2r<\/strong> ).<\/li>\n\n\n\n<li><strong>Circumference<\/strong> \u279c The distance around the circle.<\/li>\n\n\n\n<li><strong>Chord<\/strong> \u279c A line segment joining two points on the circle.<\/li>\n\n\n\n<li><strong>Arc<\/strong> \u279c A part of the circumference.<\/li>\n\n\n\n<li><strong>Sector<\/strong> \u279c A &#8220;pizza slice \ud83c\udf55&#8221; shaped region.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udccf <strong>Circumference Formulas<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Using <strong>radius<\/strong>:<br>\ud83d\udc49 <strong>C = 2\u03c0r<\/strong><\/li>\n\n\n\n<li>Using <strong>diameter<\/strong>:<br>\ud83d\udc49 <strong>C = \u03c0d<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe0 <strong>Area of a Circle<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Formula:<br>\ud83d\udc49 <strong>A = \u03c0r\u00b2<\/strong><\/li>\n\n\n\n<li>Remember: Square the radius first! \ud83e\udde0\u2728<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd22 <strong>Arc Length (L)<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For an arc with <strong>central angle \u03b8 (in degrees)<\/strong>:<br>\ud83d\udc49 <strong>L = (\u03b8 \/ 360\u00b0) \u00d7 Circumference<\/strong><\/li>\n\n\n\n<li>Part of the circle = part of the circumference! \ud83d\udd04<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83c\udf55 <strong>Area of a Sector<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Formula:<br>\ud83d\udc49 <strong>Area\u209b\u2091c\u209c\u2092\u1d63 = (\u03b8 \/ 360\u00b0) \u00d7 \u03c0r\u00b2<\/strong><\/li>\n\n\n\n<li>It\u2019s like taking a slice of the full circle\u2019s area. \ud83e\udd67<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd3a <strong>Relationship Between Radius &amp; Diameter<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If radius is known \u2192 find diameter: <strong>d = 2r<\/strong><\/li>\n\n\n\n<li>If diameter is known \u2192 find radius: <strong>r = d \u00f7 2<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udcc9 <strong>Using \u03c0 Values<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For simple questions: use <strong>\u03c0 = 22\/7<\/strong><\/li>\n\n\n\n<li>For accuracy: use <strong>\u03c0 = 3.14<\/strong> or leave answer in <strong>\u03c0 form<\/strong>.<\/li>\n\n\n\n<li>Example: <strong>14\u03c0 cm<\/strong> \u2714\ufe0f is acceptable.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83e\uddee <strong>Mixed Review Tips<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify what is given: <strong>r? d? \u03b8?<\/strong><\/li>\n\n\n\n<li>Choose the correct formula.<\/li>\n\n\n\n<li>Check if the angle is a <strong>fraction of the circle<\/strong>.<\/li>\n\n\n\n<li>Keep units consistent (cm\u00b2 for area, cm for circumference).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83c\udf08 <strong>Real-Life Applications<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Designing wheels \ud83d\udeb2<\/li>\n\n\n\n<li>Circular tracks \ud83c\udfc3\u200d\u2642\ufe0f<\/li>\n\n\n\n<li>Pizza slices \ud83c\udf55<\/li>\n\n\n\n<li>Clock faces \ud83d\udd52<\/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:#e5b2b2\"><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-706e2e92a41428302b5076de2ba6c65d\" style=\"color:#b00012\"><strong>The&nbsp;diameter of a circle is&nbsp;16&nbsp;centimetres. What is the angle measure of an arc bounding a sector with area&nbsp;8\u200b\ud835\udf0b square&nbsp;centimetres?<\/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-15.png\" alt=\"\" class=\"wp-image-11815\" 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>________\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;arc&#8217;s measure can be found from the sector&#8217;s area and the circle&#8217;s area. You already know that the sector&#8217;s area is&nbsp;8\u200b\ud835\udf0bsquare centimetres, so find the circle&#8217;s&nbsp;area.<\/p>\n\n\n\n<p>To&nbsp;find the area, first find the&nbsp;radius.<\/p>\n\n\n\n<p>d   =  2r<\/p>\n\n\n\n<p>16  = 2r      Plug&nbsp;in&nbsp;d=16<\/p>\n\n\n\n<p>8   =  r       Divide&nbsp;both sides by&nbsp;2<\/p>\n\n\n\n<p>The&nbsp;radius is&nbsp;8&nbsp;centimetres.<\/p>\n\n\n\n<p>Next,&nbsp;find the area of the&nbsp;circle.<\/p>\n\n\n\n<p>A =  \u200b\ud835\udf0br<sup>2<\/sup><br>   =   \u200b\ud835\udf0b . 8<sup>2<\/sup>     Plug in r=8<br>   =  64 \u200b\ud835\udf0b       Square<\/p>\n\n\n\n<p>The&nbsp;area of the circle is&nbsp;64\u200b\ud835\udf0b square&nbsp;centimetres.<\/p>\n\n\n\n<p>Finally,&nbsp;find the angle measure of the&nbsp;arc.<\/p>\n\n\n\n<p>K = A . m\/360<\/p>\n\n\n\n<p> 8\u200b\ud835\udf0b   = 64 \ud835\udf0b   m\/ 360     Plug&nbsp;in&nbsp;K=8\u200b\ud835\udf0b&nbsp;and&nbsp;A=64\ud835\udf0b<\/p>\n\n\n\n<p> 8\u200b\ud835\udf0b . 360 \/ 64 \ud835\udf0b  =m  Multiply<em>&nbsp;<\/em>both sides by 360 \/ 64 \ud835\udf0b<\/p>\n\n\n\n<p>45 = m        Multiply&nbsp;and&nbsp;simplify<\/p>\n\n\n\n<p>The&nbsp;angle measure of the arc is&nbsp;45\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9af4c4\"><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-42f2b80be3cdf1c07928c617ba3eb2e0\" style=\"color:#b00012\"><strong>The Radius of a circle is 7 metres . what is the area ?<\/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-14.png\" alt=\"\" class=\"wp-image-11796\" style=\"width:326px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give&nbsp;the exact answer in simplest&nbsp;form.<\/p>\n\n\n\n<p>_______ square metres<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the area.<br>A =  \u200b\ud835\udf0br<sup>2<\/sup><br>   =   \u200b\ud835\udf0b.7<sup>2<\/sup>     Plug in r=7<br>   =  49\u200b\ud835\udf0b       Square<br>The area is 49\u200b\ud835\udf0b square metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9adde6\"><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-9e7cfdd53b4bec1d267c318eb38aba37\" style=\"color:#b00012\"><strong>The&nbsp;circumference of a circle is&nbsp;4\u200b\ud835\udf0b  metres. What is the&nbsp;area?<\/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-16.png\" alt=\"\" class=\"wp-image-11834\" style=\"width:332px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Give&nbsp;the exact answer in simplest&nbsp;form.<\/p>\n\n\n\n<p>_______ square metres<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;find the&nbsp;radius.<\/p>\n\n\n\n<p>C = 2\ud835\udf0br<\/p>\n\n\n\n<p>4\ud835\udf0b  =  2\ud835\udf0br          Plug&nbsp;in&nbsp;C=4\u200b\ud835\udf0b<\/p>\n\n\n\n<p>2  =  r        Divide&nbsp;both sides by&nbsp;2\u200b\ud835\udf0b<\/p>\n\n\n\n<p>The&nbsp;radius is&nbsp;2&nbsp;metres.<\/p>\n\n\n\n<p>Now,&nbsp;find the&nbsp;area.<\/p>\n\n\n\n<p>A =  \u200b\ud835\udf0br<sup>2<\/sup><br>   =   \u200b\ud835\udf0b.2<sup>2<\/sup>     Plug in r=2<br>   =  4 \u200b\ud835\udf0b       Square<\/p>\n\n\n\n<p>The&nbsp;area is&nbsp;4\u200b\ud835\udf0b&nbsp;square&nbsp;metres.<\/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\/88995\/857\/571\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-68.png\" alt=\"\" class=\"wp-image-7889\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-68.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-68-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-68-150x150.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\/88994\/588\/897\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-77.png\" alt=\"\" class=\"wp-image-7890\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-77.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-77-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-77-150x150.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:#c81ac6\"><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Circle measurements: mixed review Key Notes : \ud83d\udd35 Parts of a Circle \ud83d\udccf Circumference Formulas \ud83d\udfe0 Area of a Circle \ud83d\udd22 Arc Length (L) \ud83c\udf55 Area of a Sector \ud83d\udd3a Relationship Between Radius &amp; Diameter \ud83d\udcc9 Using \u03c0 Values \ud83e\uddee Mixed Review Tips \ud83c\udf08 Real-Life Applications Learn with an example The&nbsp;diameter of a circle is&nbsp;16&nbsp;centimetres.<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/l-5-circle-measurements-mixed-review\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.5 Circle measurements: mixed review&#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-202","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202","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=202"}],"version-history":[{"count":17,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202\/revisions"}],"predecessor-version":[{"id":18286,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202\/revisions\/18286"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}