An outdoor decorative pond in the shape of a hemispherical tank is to be filled with water pumped into the tank through an inlet in its bottom. Suppose that the radius of the tank is R = 10 ft, that water is pumped in at a rate of T ft/min, and that the tank is initially empty. As the tank fills, it loses water through evaporation. Assume that the rate of evaporation is proportional to the area A of the surface of the water and that the constant of proportionality is k = 0.01. Output: water evaporates at rate proportional to area A of surface FR- Input: water pumped in at rate 7 ft/min (a) hemispherical tank (b) cross-section of tank (a) The rate of change of the volume of the water at time t is a net rate. Use this net rate to determine a differential equation for the height h of the water at time t. The volume of the water shown in the figure is V = TRh -Th, where R = 10. Express the area of the surface of the water A = Tr in terms of h. (b) Solve the differential equation in part (a). h(t) = Graph the solution.