Ex 6.1

Chapter 6 Class 12 Application of Derivatives
Serial order wise

### Transcript

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๐จ/๐๐ when r = 10 cm We know that Area of circle = ฯr2 A = ฯr2 Differentiating w.r.t time ๐๐จ/๐๐ = ๐(๐๐๐)/๐๐ ๐๐ด/๐๐ก = ฯ ๐(๐2)/๐๐ก ๐๐ด/๐๐ก = ฯ ๐(๐2)/๐๐ก ร ๐๐/๐๐ ๐๐ด/๐๐ก = ฯ ๐(๐๐)/๐๐ ร ๐๐/๐๐ก ๐๐ด/๐๐ก = ฯ. 2r . ๐๐/๐๐ก ๐๐ด/๐๐ก = 2ฯr . ๐๐/๐๐ ๐๐ด/๐๐ก = 2ฯr . 3 ๐๐ด/๐๐ก = 6ฯr When ๐ = 10 cm โ ๐๐ด/๐๐กโค|_(๐ =10) = 6 ร ฯ ร 10 โ ๐๐ด/๐๐กโค|_(๐ =10) = 60 ฯ (From (1): ๐๐/๐๐ก = 3) Since area is in cm2 & time is in sec ๐๐ด/๐๐ก = 60ฯ cm2/sec Hence, Area is increasing at the rate of 60ฯ cm2/sec when r = 10 cm