2021 VJC P1 Q4

Water is poured at a rate of \(8\)cm\(^{3}\) per second into a conical container with base radius \(8\)cm. The semi-vertical angle of the cone is \(\theta \), where \(\tan \theta =0.4\). At time \(t\) seconds after the start, the radius of the water surface is \(x\)cm (see diagram). Find the rate of increase of the depth of water when the depth is \(10\)cm.

[The volume of a cone of base radius \(r\) and height \(h\) is given by \(V=\frac{1}{3}\pi {{r}^{2}}h\)].[7]