2025 TMJC P1 Q6

[It is given that the volume of a circular cone with base radius \(r\) and height \(h\) is \(\frac{1}{3} \pi r^2 h\).]
A container is made in the shape of an inverted open right circular cone. The height of the container is \(6\) metres, and the radius is \(2\) metres. The container is initially empty. Water is poured into the container while, at the same time, water is leaking from a hole at the bottom of the container at a rate of \(0.03\) m\({}^3\)/s, resulting in the depth of water in the container to be increasing at a rate of \(0.1\) m/s. At time \(t\) seconds after the start, the depth of water in the container is \(h\) metres.

1. Find, in terms of \(h\), an expression for the volume of water in the container at time \(t\) seconds after the start.[2]
2. Find the rate at which water is being poured into the container when the depth of water in the container is \(3\) metres.[4]