1.47: Past-paper question 11

Figure 3 shows a hollow right circular cone with radius 3 metres and height 4 metres above the vertex $\displaystyle A$

The cone is fixed with its axis of symmetry vertical.
The cone is initially empty.

Water pours into the cone at a constant rate of $\displaystyle 9\pi \mathrm{m}^3/\mathrm{s}$

At time $\displaystyle t$ seconds after the water starts to pour into the cone, the height of the water is $\displaystyle h$ metres above $\displaystyle A$

Find, in $\displaystyle \mathrm{m}/\mathrm{s}$, the rate at which the height of the water is increasing at the instant when $\displaystyle h = 2$