3.121: Related rates for a cylinder's curved surface

A cylinder, open at both ends, has base radius $r\,\mathrm{cm}$ and height $4r\,\mathrm{cm}$. Its curved surface area is $S\,\mathrm{cm}^{2}$. Given that $r$ varies with time $t$, find $S$ at the instant when $\dfrac{\mathrm{d}S}{\mathrm{d}t} = 6\dfrac{\mathrm{d}r}{\mathrm{d}t}$.