{"id":335,"date":"2022-04-13T10:43:25","date_gmt":"2022-04-13T10:43:25","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=335"},"modified":"2025-01-03T11:53:21","modified_gmt":"2025-01-03T11:53:21","slug":"r-3-arc-measure-and-arc-length","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/r-3-arc-measure-and-arc-length\/","title":{"rendered":"R.3 Arc measure and arc length"},"content":{"rendered":"\n

Arc measure and arc length<\/strong><\/h2>\n\n\n\n

Key Notes :<\/p>\n\n\n\n

The formula for the length of an arc is.<\/p>\n\n\n\n

\ud835\udcc1 = m \/ 360 . c<\/p>\n\n\n\n

where \ud835\udcc1 is the arc length, C is the circumference, and m is the measure of the arc in degrees.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
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\ud83d\udd14 The radius of a circle is 3 metres. What is the length of a 90\u00b0 arc?<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Give the exact answer in simplest form.
________ metres<\/p>\n<\/div><\/div>\n\n\n\n

The arc’s length depends on the arc’s measure and the circle’s circumference. You already know that the arc’s measure is 90\u00b0, so find the circle’s circumference.<\/p>\n\n\n\n

First, find the circumference.<\/p>\n\n\n\n

C = 2\u200b\ud835\udf0br<\/p>\n\n\n\n

= 2\u200b\ud835\udf0b(3) Plug in r=3<\/p>\n\n\n\n

= 6\u200b\ud835\udf0b Multiply<\/p>\n\n\n\n

The circumference is 6\u200b\ud835\udf0b metres.
Now, find the length of the arc.<\/p>\n\n\n\n

\ud835\udcc1 = C . m \/ 360<\/p>\n\n\n\n

= 6\u200b\ud835\udf0b . 90 \/ 360 Plug in C=6\u200b\ud835\udf0b and m=90<\/p>\n\n\n\n

= 3\u200b\ud835\udf0b \/ 2 Multiply and simplify<\/p>\n\n\n\n

The length of the arc is 3\u200b\ud835\udf0b \/ 2 metres<\/p>\n<\/div><\/div>\n\n\n\n

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\n

\ud83d\udd14 The radius of a circle is 5 kilometres. What is the length of a 135\u00b0 arc?<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Give the exact answer in simplest form.
________ kilometres<\/p>\n<\/div><\/div>\n\n\n\n

The arc’s length depends on the arc’s measure and the circle’s circumference. You already know that the arc’s measure is 135\u00b0, so find the circle’s circumference.<\/p>\n\n\n\n

First, find the circumference.<\/p>\n\n\n\n

C = 2\u200b\ud835\udf0br<\/p>\n\n\n\n

= 2\u200b\ud835\udf0b(5) Plug in r=5<\/p>\n\n\n\n

= 10\u200b\ud835\udf0b Multiply<\/p>\n\n\n\n

The circumference is 10\u200b\ud835\udf0b kilometres.<\/p>\n\n\n\n

Now, find the length of the arc.<\/p>\n\n\n\n

\ud835\udcc1=C . m \/ 360<\/p>\n\n\n\n

= 10\u200b\ud835\udf0b . 135 \/ 360 Plug in C=10\u200b\ud835\udf0b and m=135<\/p>\n\n\n\n

= 15\ud835\udf0b \/ 4 Multiply and simplify<\/p>\n\n\n\n

The length of the arc is 15\ud835\udf0b \/ 4 kilometres.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\ud83d\udd14 The radius of a circle is 10 centimetres. What is the length of a 135\u00b0 arc?<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Give the exact answer in simplest form. <\/p>\n\n\n\n

________ centimetres<\/p>\n<\/div><\/div>\n\n\n\n

The arc’s length depends on the arc’s measure and the circle’s circumference. You already know that the arc’s measure is 135\u00b0, so find the circle’s circumference.<\/p>\n\n\n\n

First, find the circumference.<\/p>\n\n\n\n

C = 2\u200b\ud835\udf0br<\/p>\n\n\n\n

= 2\u200b\ud835\udf0b(10) Plug in r=10<\/p>\n\n\n\n

= 20\u200b\ud835\udf0b Multiply<\/p>\n\n\n\n

The circumference is 20\u200b\ud835\udf0b centimetres.<\/p>\n\n\n\n

Now, find the length of the arc.<\/p>\n\n\n\n

\ud835\udcc1 = C . m \/ 360<\/p>\n\n\n\n

=20\u200b\ud835\udf0b<\/strong> . 135 \/ 360 Plug in C=20\u200b\ud835\udf0b and m=135<\/p>\n\n\n\n

= 15\u200b\ud835\udf0b \/ 2 Multiply and simplify<\/p>\n\n\n\n

The length of the arc is 15\u200b\ud835\udf0b \/ 2 centimetres.<\/p>\n<\/div><\/div>\n\n\n\n

Let’s practice!<\/p>\n\n\n\n

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\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
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\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Arc measure and arc length Key Notes : The formula for the length of an arc is. \ud835\udcc1 = m \/ 360 . c where \ud835\udcc1 is the arc length, C is the circumference, and m is the measure of the arc in degrees. Learn with an example \ud83d\udd14 The radius of a circle is 3 metres. What is theContinue reading “R.3 Arc measure and arc length”<\/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-335","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=335"}],"version-history":[{"count":11,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/335\/revisions"}],"predecessor-version":[{"id":17357,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/335\/revisions\/17357"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}