2022 BTYSS P1 Q11

A container, initially empty, is filled with water. After \(t\) seconds, the depth of water in the container is \(h\) cm and the volume of water, \(V\text{ cm}^3\), is given by \[V=\dfrac\pi8h^2(3+h).\] Given that the volume of water increases at a constant rate and that \(h=6\) when \(t=4\), find

1. the constant rate of change of the volume of water,[3]
2. the rate of change of the depth of water at the instant when \(h=2\).[4]