A balloon which always remains spherical has variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

The correct answer is $400 \pi$ $cm^2/sec$

Volume of a sphere V = $\dfrac{4}{3} \pi r^3$

$\dfrac{dV}{dr}$ = $\dfrac{d}{dr}$ $( \dfrac{4}{3} \pi r^3 )$ = $ \dfrac{4}{3} \pi (3r^2)$ = $4 \pi r^2$


When the radius is 10 cm, $\dfrac{dV}{dr}$ = $4 \pi (10)^2$ = $400 \pi$ $cm^2/sec$