2020 VJC Promo Q5

The diagram below shows a drain in the form of a triangrlar prism \(8\)m long and \(2\)m deep. The opening of the drain is \(1.5\)m wide.

During a heavy downpour, rainwater flows into the drain at a constant rate of \(0.03\)m\(^{3}\) per second. At the same time, the rainwater is drained away at a constant rate of \(0.02\) m\(^{3}\) per second. At time \(t\) seconds after the start, the depth of the rainwater in the drain is \(h\) m.

1. Show that the volume of rainwater in the drain. \(V\)m\(^{3}\), is given by \(V=3{{h}^{2}}\).[3]
2. Find the rate at which \(h\) is increasing when \(V=7.2\).[4]