The volume of a cube grows at 9 cm³/s. How fast is each edge growing when the edge is 3 cm long?

Explanation

1. 01

   $V = a^3$, so $\frac{dV}{dt} = 3a^2\frac{da}{dt}$.

2. 02

   $9 = 3 \times 9 \times \frac{da}{dt}$, so $\frac{da}{dt} = \frac{1}{3}$ cm/s.