(CIE 0606/2021/m/22/Q5)
A cube of side $x \mathrm{~cm}$ has surface area $S \mathrm{~cm}^{2}$. The volume, $V \mathrm{~cm}^{3}$, of the cube is increasing at a rate of $480 \mathrm{~cm}^{3} \mathrm{~s}^{-1}$. Find, at the instant when $V=512$,
(a) the rate of increase of $x$,
(b) the rate of increase of $S$.
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