The radius of a spherical balloon grows at 1 cm/s. How fast is its volume growing when the radius is 3 cm?

Explanation

1. 01

   $V = \frac{4}{3}\pi r^3$, so $\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$.

2. 02

   $4\pi \times 9 \times 1 = 36\pi$ cm³/s.