The radius of a soap bubble grows at 0.5 cm/s. How fast is its surface area growing when the radius is 5 cm?

Explanation

1. 01

   $S = 4\pi r^{2}$, so $\frac{dS}{dt} = 8\pi r\frac{dr}{dt}$.

2. 02

   $8\pi \times 5 \times 0.5 = 20\pi$ cm²/s.