9. [12 marks]

A conical tank rests on a platform that is 10 meters above a large lake. The circular base of the tank has a radius of 4 meters and the top of the tank is 15 meters above the surface of the lake. How much work must be done to fill the tank with water from the lake if it is to be pumped in through an outlet at the bottom of the tank?

Set up your coordinate system so that = 0 corresponds to the top of the tank and = 5 corresponds to the base of the tank, which rests on the platform. Use the fact that the density of water is 1000 kg/m^3 and = 9.8 m/s^2.