Problem 3 (20 marks) A spherical water tank with an inner radius of / metres has its lowest point / metres above the ground. It is filled by a pipe that feeds the tank at its lowest point. inflow pipe Neglecting the volume of the inflow pipe and writing p for the density of water, determine the amount of work W required to fill the tank if it is initially empty. Apply the five-step slicing method in complete detail. You may leave your final answer as a definite integral