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The volume of a ball increases at $2 π c . c / \sec$ . The rate of increase of radius when the volume is $288 π$ c.c is

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$\frac{1}{36} c m / \sec$

$\frac{1}{72} c m / \sec$

$\frac{1}{18} c m / \sec$

$\frac{1}{9} c m / \sec$

answer is B.

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Detailed Solution

$v = 288 π, \frac{d v}{d t} = 2 π c . c / \sec$

$v = \frac{4}{3} π r^{3} \Rightarrow r = 6$

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