(A Math) 2025 CCHY PRELIMS P1 Q2

A container has a capacity of \(840\text{ cm}^3\) and is initially filled completely with water. The volume, \(V\text{ cm}^3\), of water in the container is given by \(V=h^2+2h\) where \(h\text{ cm}\) is the height of the water level in the container. Due to leakage at the bottom of the container, the height of the water level in the container decreases at a rate of \(\frac{5t}{3}\text{ cm/s}\), where \(t\) is the time in seconds.

1. Find the initial height of the water level in the container.[2]
2. Show that the height of the water level \(h\) can be expressed as \(h=-\frac{5t^2}{6}+28\).[2]
3. Find the rate of decrease of volume when \(t=3\).[5]