# Ex 6.1,1 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

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

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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.