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



  1. Chapter 6 Class 12 Application of Derivatives
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Example 49 A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm. Let A be the area & radius of circular disc A = ฯ€r2 Given radius increases at 0.05 cm/s ๐‘‘๐‘Ÿ/๐‘‘๐‘ก = 0.05cm/s We need to find the rate at which its area is increasing i.e. ๐‘‘๐ด/๐‘‘๐‘ก Now, ๐‘‘๐ด/๐‘‘๐‘ก = ๐‘‘(๐œ‹๐‘Ÿ2)/๐‘‘๐‘ก = ฯ€ . ๐‘‘๐‘Ÿ2/๐‘‘๐‘ก = ฯ€ . ๐‘‘๐‘Ÿ2/๐‘‘๐‘Ÿ . ๐‘‘๐‘Ÿ/๐‘‘๐‘ก = ฯ€ (2๐‘Ÿ) ๐‘‘๐‘Ÿ/๐‘‘๐‘ก We need to find rate at which area is increasing when radius = 3.2cm Putting r = 2 and ๐‘‘๐‘Ÿ/๐‘‘๐‘ก = 0.05 ๐‘‘๐ด/๐‘‘๐‘ก = ฯ€ . 2 ร— (3.2) ร— 0.05 = 0.320ฯ€ Since area is in cm2 & time is in seconds ๐’…๐‘จ/๐’…๐’• = 0.320ฯ€ cm2/s

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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.