Problem3 A metallic sphere (initial radius r0, density ps ) is suspended above a cylindrical tank already containing the same metal in liquid state (density pi). The tank's diameter is D and the initial level of the liquid metal in the tank is h0. The sphere is melting slowly, and its diameter is decreasing at a constant rate a(m/s). Determine: (a) the expression for the variation of the sphere's radius with time, (b) the expression for the increase with time of the level of the liquid metal in the tank resulting from the melting sphere, (c) the final height of the liquid metal in the tank once the sphere is completely melted. Check your answer by a global mass balance