2021 RI P1 Q2

A tank containing water is in the form of a cone with vertex \(C\). The axis is vertical and the semi-vertical angle is \({{60}^{\circ }}\), as shown in the diagram. At time \(t=0\), the tank is filled with \(94\pi \)cm\(^{3}\) of water. At this instant, a tap at \(C\) is turned on and water begins to flow out at a constant rate of \(2\pi \)cm\(^{3}\)s\(^{-1}\). Denoting \(h\) cm as the depth of water at time \(t\)s, find the rate of decrease of \(h\) when \(t=15\), leaving your answer in exact form.[4]

[The volume \(V\) of a cone of vertical height \(h\) and base radius \(r\) is given by \(V=\frac{1}{3}\pi {{r}^{2}}h\).]