Question

The rate of change of the surface area of a sphere of radius $r$ when the radius is increasing at the rate of $2\, cm / \sec$ is proportional to

• A. $\frac{1}{r^{2}}$
• B. $\frac{1}{r}$
• C. $r^{2}$
• D. $r$

Answer 1

Answer: (D)

Surface area of the sphere is $s=4 \pi r^{2}\, \&\, \frac{d r}{d t}=2$
$\frac{d s}{d t}=8 \pi r \frac{d r}{d t}$
$=8 \pi r(2)$
$=16 \pi r$
$\therefore \frac{d s}{d t} \propto r$