2024 JPJC Promo Q2

Water is poured at a rate of \(0.1\)m\(^{3}\) per minute into a container in the form of an open cone. The semi-vertical angle of the cone is \({{30}^{{}^\circ }}\). At time \(t\) minutes after the start, the radius of the water surface is \(r\) m (see diagram). Find the rate of increase of the depth of water when the volume of the water is \(3\)m\(^{3}\).[5]

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