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Application Of Derivatives

Question

Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm.

Solution

Let A be area of circle of radius r

therefore space space space space space space space space space space space straight A space equals space πr squared

Rate of change of area with respect to

straight r space equals space dA over dr

equals space straight d over dr left parenthesis πr squared right parenthesis space equals space 2 πr

when r = 5, rate of change of area =

2 straight pi space cross times space 5 space equals space 10 straight pi space cm squared divided by cm