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Last updated at July 18, 2019 by Teachoo

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Ex 6.1,1 Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm Radius of circle = ๐ & let A be the area of circle We need to find rate of change of Area w. r. t Radius i.e. we need to calculate ๐๐ด๏ทฎ๐๐๏ทฏ We know that Area of Circle = ๐๐๏ทฎ2๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = ๐ ๐๐๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐๐๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = ๐ ๐ (๐๏ทฎ2๏ทฏ)๏ทฎ๐๐๏ทฏ๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = ๐ 2๐๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = 2๐ ๐ โข when r = 3 cm ๐๐ด๏ทฎ๐๐๏ทฏ = 2rฯ Putting r = 3 cm ๐๐ด๏ทฎ๐๐๏ทฏ๏ทฏ๏ทฎ๐ = 3๏ทฏ= 2(3) ฯ ๐๐ด๏ทฎ๐๐๏ทฏ๏ทฏ๏ทฎ๐ = 3๏ทฏ = 6 ฯ Since Area is in cm2 & radius is in cm ๐๐ด๏ทฎ๐๐๏ทฏ = 6ฯ ๐๐๐๏ทฎ๐๐๏ทฏ Hence Area is increasing at the rate of 6ฯ cm2/ cm when r = 3 cm (ii) r = 4 cm ๐๐ด๏ทฎ๐๐๏ทฏ = 2rฯ Putting r = 4 cm ๐๐ด๏ทฎ๐๐๏ทฏ = 2(4)ฯ ๐๐ด๏ทฎ๐๐๏ทฏ = 8 ฯ Since Area is in cm2 & radius is in cm ๐ ๐จ๏ทฎ๐ ๐๏ทฏ = 8ฯ ๐๐๐๏ทฎ๐๐๏ทฏ Hence Area is increasing at the rate of 8ฯ cm2/cm when r = 4 cm

Chapter 6 Class 12 Application of Derivatives

Serial order wise

About the Author

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.