Chapter 3 - Differentiation - 3.9 Related Rates - Exercises - Page 159: 5

$27000\pi\,cm^{3}/min $

$\frac{dV}{dt}=\frac{dV}{dr}\times\frac{dr}{dt}$ $=\frac{d}{dr}(\frac{4}{3}\pi r^{3})\times30\,cm/min $ $=\frac{4}{3}\times3\times\pi r^{2}\times 30\,cm/min $ $=120\pi r^{2}\, cm/min $ $=120\pi(15\,cm)^{2}\,cm/min $ $=27000\pi\,cm^{3}/min $