Finding rate of change

Chapter 6 Class 12 Application of Derivatives
Concept wise

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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 cmLet Radius of circle = ๐ & Area of circle = A We need to find rate of change of Area w. r. t Radius i.e. we need to calculate ๐๐จ/๐๐ We know that Area of Circle = A = ใ๐๐ใ^2 Finding ๐๐จ/๐๐ ๐๐ด/๐๐ = (๐ (ใ๐๐ใ^2 ))/๐๐ ๐๐ด/๐๐ = ๐ (๐ใ(๐ใ^2))/๐๐ ๐๐ด/๐๐ = ๐(2๐) ๐๐จ/๐๐ = ๐๐๐ When r = 3 cm ๐๐ด/๐๐ = 2ฯr Putting r = 3 cm โ ๐๐ด/๐๐โค|_(๐ = 3)= 2ฯ ร 3 โ ๐๐ด/๐๐โค|_(๐ = 3) = 6ฯ Since Area is in cm2 & radius is in cm ๐๐ด/๐๐ = 6ฯ cm2/cm Hence, Area is increasing at the rate of 6ฯ cm2/ cm when r = 3 cm (ii) When r = 4 cm ๐๐ด/๐๐ = 2ฯr Putting r = 4 cm ๐๐ด/๐๐ = 2ฯ ร 4 ๐๐ด/๐๐ = 8ฯ Since Area is in cm2 & radius is in cm ๐๐จ/๐๐ = 8ฯ cm2/cm Hence, Area is increasing at the rate of 8ฯ cm2/cm when r = 4 cm