Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Ex 6.1, 6 - Radius of a circle is increasing at rate of 0.7 cm/s - Finding rate of change


  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.1,6 The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference? Let r be the radius of circle & C be the circumference of circle Given that Radius of a circle is increasing at the rate of 0.7 cm/sec i.e. ๐‘‘๐‘Ÿ๏ทฎ๐‘‘๐‘ก๏ทฏ = 0.7 cm/sec We need find rate of change of circumference of circle w. r. ๐‘ก time i.e. we need to calculate ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ we know that Circumference of circle = 2ฯ€r i.e. C = 2ฯ€r Different w. r. t time ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = ๐‘‘(2๐œ‹๐‘Ÿ)๏ทฎ๐‘‘๐‘ก๏ทฏ ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 2ฯ€ ๐‘‘๐‘Ÿ๏ทฎ๐‘‘๐‘ก๏ทฏ ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 2ฯ€ ร— 0.7 ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 1.4 ฯ€ Since circumference is in cm & time is in sec ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 1.4ฯ€ ๐‘๐‘š๏ทฎ๐‘ ๐‘’๐‘๏ทฏ ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 1.4ฯ€ cm/sec Hence, circumference of circle is increasing at the rate of 1.4ฯ€cm/sec

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.