Differentiation

An inverted conical container has height \(12\text{ cm}\) and rim radius \(6\text{ cm}\). Water enters at \(9\pi\text{ cm}^3/\text{s}\).

1. Show that \(V=\dfrac{\pi h^3}{12}\).

2. Find \(\dfrac{\mathrm{d}h}{\mathrm{d}t}\) when \(h=6\text{ cm}\).