A spherical balloon is inflated at a rate of $100\pi$ cm$^3$/s. How fast is its radius increasing when the radius is 5 cm?

Core Concept

Differentiating $V=\dfrac{4}{3}\pi r^3$ gives $\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}$. Solving $100\pi=4\pi(25)\dfrac{dr}{dt}$ gives $\dfrac{dr}{dt}=1$ cm/s.