Question

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

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

Answer 1

Answer: (D)

$r$

Given $\frac{dr}{dt}=2cm/sec$

Surface area of sphere $S=4\pi r^2$

$\frac{dS}{dt}=8\pi r\frac{dr}{dt}$

$\Rightarrow \frac{dS}{dt}=16\pi r$

$\Rightarrow$ Rate of change of surface area $\propto$ radius of sphere.