2016 JJC Promo Q10

If \(V\), \(r\) and \(h\) all vary with time \(t\) , find an expression for \(\frac{\mathrm{d}V}{\mathrm{d}t}\) in terms of \(r\), \(h\), \(\frac{\mathrm{d}r}{\mathrm{d}t}\) and \(\frac{\mathrm{d}h}{\mathrm{d}t}\).[2]

Given that the radius is increasing at a constant rate of \(3\) cm s\(^{-1}\) while the height is decreasing at a constant rate 2 cm s\(^{-1}\), find the rate of change of the volume when the radius is \(20\) cm and the height is \(30\)cm.[2]