Question

The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is $2$ cm is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Volume of sphere $V=\frac{4}{3}\pi r^3$
$\Rightarrow \frac{dV}{dr}=4\pi r^2$
Surface area of sphere, $S=4\pi r^2$
$\Rightarrow \frac{dS}{dr}=8\pi r$

$\Rightarrow \frac{dV/dr}{dS/dr}=\frac{dV}{dS}=\frac{r}{2}$
$\Rightarrow \frac{dV}{dS}=1$ for $r=2$