Last updated at April 19, 2021 by Teachoo

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Ex 6.1, 3 The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.Let r be the radius of circle . & A be the Area of circle. Given that Radius of a circle is increasing at the rate of 3 cm/s Thus, ๐ ๐/๐ ๐ = 3 cm /sec We need to find rate of change of area of circle w. r. t time when r = 10 cm i.e. we need to find ๐ ๐จ/๐ ๐ when r = 10 cm We know that Area of circle = ฯr2 A = ฯr2 Differentiating w.r.t time ๐ ๐จ/๐ ๐ = ๐ (๐ ๐๐)/๐ ๐ ๐๐ด/๐๐ก = ฯ ๐(๐2)/๐๐ก ๐๐ด/๐๐ก = ฯ ๐(๐2)/๐๐ก ร ๐ ๐/๐ ๐ ๐๐ด/๐๐ก = ฯ ๐ (๐๐)/๐ ๐ ร ๐๐/๐๐ก ๐๐ด/๐๐ก = ฯ. 2r . ๐๐/๐๐ก ๐๐ด/๐๐ก = 2ฯr . ๐ ๐/๐ ๐ ๐๐ด/๐๐ก = 2ฯr . 3 ๐๐ด/๐๐ก = 6ฯr When ๐ = 10 cm โ ๐๐ด/๐๐กโค|_(๐ =10) = 6 ร ฯ ร 10 โ ๐๐ด/๐๐กโค|_(๐ =10) = 60 ฯ (From (1): ๐๐/๐๐ก = 3) Since area is in cm2 & time is in sec ๐๐ด/๐๐ก = 60ฯ cm2/sec Hence, Area is increasing at the rate of 60ฯ cm2/sec when r = 10 cm

Ex 6.1

Ex 6.1, 1
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Chapter 6 Class 12 Application of Derivatives (Term 1)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.