Question

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

• A. $24\pi$
• B. $32\pi$
• C. $16\pi$
• D. $8\pi$

Answer 1

Answer: (C)

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