A cube of side \(x\text{ cm}\) has surface area \(S\text{ cm}^2\). The volume, \(V\text{ cm}^3\), of the cube is increasing at a rate of \(480\text{ cm}^3\text{ s}^{-1}\). Find, at the instant when \(V=512\),

(a) the rate of increase of \(x\),

(b) the rate of increase of \(S\).