What is the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ $c m$ .

12 π

c m

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16 π

c m

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18 π

c m

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24 π

c m

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Solution

The correct option is C $12 π$ $c m$
Given, $r = 6$ $c m$
Area of a circle with radius $r$ is, $A = π r^{2}$
$\Rightarrow \frac{d A}{d r} = 2 π r$
At $r = 6 c m$ ,
$\frac{d A}{d r} = 2 π (6) = 12 π c m$

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