Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

$V=\frac{4}{3}\pi r^3,S=4\pi r^2$
$\frac{dV}{dr}=4\pi r^2,\frac{dS}{dr}=8\pi r$
$\therefore \frac{dV}{dS}=\frac{dV/dr}{dS/dr}=\frac{4\pi r^2}{8\pi r}=\frac{r}{2}$
When $r=2,\frac{dV}{dS}=\frac{2}{2}=1$