If a spherical tank of radius 2 feet has h feet of water present in the tank, then the volume of water in the tank is given by the formula V = π 3 h 2 (4 − h). (a) At what instantaneous rate is the volume of water in the tank changing with respect to the height of the water at the instant h = 1? What are the units on this quantity? (b) Now suppose that the height of water in the tank is being regulated by an inflow and outflow (e. g., a faucet and a drain) so that the height of the water at time t is given by the rule h(t) = cos(πt) + 1 where t is measured in hours (and h is still measured in feet). At what rate is the height of the water changing with respect to time at the instant t = 1 2 ? (c) Continuing under the assumptions in (b), at what instantaneous rate is the volume of water in the tank changing with respect to time at the instant t = 1 2 ? (d) What are the main differences between the rates found in (a) and (c)? Include a discussion of the relevant units.