1) 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 A) 0 B) 2 C) 8 D) 9 Answer: Option CExplanation: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; $\frac{dv}{dt}=4\pi (10)^{2}.(0.02) = 8\pi cm^{3}/s$.
