A water tank that is in the shape of a sphere has a radius of 4 meters. When the tank is filled to a depth of

h meters, the volume of water in the tank is

V

=p/3 h^2(12 − h).

h is the height of water, measured in meters from the bottom of the tank.

*What values of h are possible.

*Suppose that the tank is initially empty but that water is poured into the tank at the constant rate of 2 cubic meters per minute. What is the total volume of the tank? How long does it take to fill the tank?

*Determine a formula for the rate of change of the height of thewater with respect to time. Your formula should only depend on h.