Discussion Forum

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___ π cm/s

Answer:

Explanation:

V = $\frac{4}{3}\pi r^{3}$

$\frac{dv}{dt}=\frac{4}{3}\pi\frac{d}{dt}r^{3}$

= $\frac{4}{3}\pi 3r^{2}\frac{dr}{dt}$ = $4\pi r^{2}\frac{dr}{dt}$

When r = 10 cm;

$\frac{dv}{dt}=4\pi (10)^{2}.(0.02) = 8\pi cm^{3}/s$.