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  4. The rate of change of volume of sphere with respect to its radius r at r=2 is .

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Q. The rate of change of volume of sphere with respect to its radius $r$ at $r=2$ is ______.

Gujarat CETGujarat CET 2020

Solution:

$V=\frac{4}{3} \pi r^{2}$
$\Rightarrow \frac{d V}{d r}=\frac{4}{3} \times 3 \pi r^{2} $
$=4 \pi r^{2}$
Now at $(r=2)=16 \pi$