A spherical balloon is being inflated at a rate of $10\pi$ cubic centimeters per second. At what rate is the radius of the balloon increasing when the radius is $5$ cm?

Core Concept

Correct. Differentiating volume gives $\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}$. Substituting $10\pi = 4\pi(5)^2 \frac{dr}{dt}$ yields $10\pi = 100\pi \frac{dr}{dt}$, so $\frac{dr}{dt} = 0.1$.