1.17: Rates of change for two cubes

The length of each side of a cube $\displaystyle S_1$ is increasing at a constant rate of $\displaystyle 0.1\,\mathrm{m\,s^{-1}}$.

(a) Find, in $\displaystyle \mathrm{m}^3\mathrm{s}^{-1}$, the rate of increase of its volume when the side length is $\displaystyle 2\,\mathrm{m}$.

The total surface area of a different cube $\displaystyle S_2$ is increasing at a constant rate of $\displaystyle 0.05\,\mathrm{m}^2\mathrm{s}^{-1}$.

(b) Find, in $\displaystyle \mathrm{m}^3\mathrm{s}^{-1}$, the rate of increase of its volume when the side length is $\displaystyle 6\,\mathrm{m}$.