The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
$10 straight pi$
$12 straight pi$
$8 straight pi$
$11 straight pi$

Solution

12 straight pi

Let A be area of circle of radius r
$therefore space space space space space space space space space straight A space equals space πr squared$
Rate of change of area w.r.t. r = $dA over dr space equals space straight d over dr left parenthesis πr squared right parenthesis space equals space 2 πr$
When r = 6, rate of change of area = $2 straight pi cross times 6 space equals space 12 space straight pi.$
$therefore space space space space left parenthesis straight B right parenthesis thin space is space correct space answer.$

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Application Of Derivatives

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
$10 straight pi$
$12 straight pi$
$8 straight pi$
$11 straight pi$

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