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Application Of Derivatives

Question
CBSEENMA12034957
Wired Faculty App

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

Solution
Let A be area of circle of radius r
therefore space space space space 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

(a) When r = 3, rate of change of area = 2straight pi × 3 = 6  cm2/cm.
(b) When r = 4, rate of change of area = 2 straight pi × 4 = 8 straight pi cm2/cm.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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