The radius of a circular patch of paint grows at 0.3 cm/s. How fast is its area growing when the radius is 10 cm?

Explanation

1. 01

   $\frac{dA}{dt} = 2\pi r\frac{dr}{dt}$.

2. 02

   $2\pi \times 10 \times 0.3 = 6\pi$ cm²/s.