2018 CJC MYE Q3

An open inverted conical trough is made of a metal sheet of fixed area of \(9\) m\(^{2}\) with negligible thickness. It is given that the conical trough has radius \(r\) m and a slant height of \(l\) m as shown in the diagram. It is given that \(r=2\)m and \(l=2\sqrt{5}\) m. Water is pumped into the empty trough at a constant rate of \(0.02\) m\(^{3}\)/min .

Find the rate at which the height of the water level is increasing at the instant when the height of the water level is \(1\) m.[4]