The area of a circle grows at $10\pi$ cm²/s. How fast is the radius growing when the radius is 5 cm?

Explanation

1. 01

   $A = \pi r^2$, so $\frac{dA}{dt} = 2\pi r\frac{dr}{dt}$.

2. 02

   $10\pi = 2\pi \times 5 \times \frac{dr}{dt}$, so $\frac{dr}{dt} = 1$ cm/s.