Differentiation - Connected Rates of Change

Water is poured at a constant rate of \(8\text{ cm}^3/\text{s}\) into a conical container (as shown in the diagram) of base radius \(8\text{ cm}\) and semi-vertical angle of the cone is \(\theta\), where \(\tan \theta = 0.4\). The radius of the water surface is \(r\text{ cm}\) and the depth of water is \(h\text{ cm}\). The container is initially empty.

1. Find the total height of the container.
2. Express \(r\) in terms of \(h\).
3. Find the rate of increase of \(h\) when \(h = 10\text{ cm}\).