Gasoline is pumped into a cylindrical tank with a radius of 16 feet and a height of 6 feet. the tank has 750 cubic feet of gasoline at time t = 0 hours. the rate at which gasoline is pumped into the tank is given by the function r, where r(t) = 1,000e ? t 2 20 cubic feet per hour for 0 ? t ? 10. during the same time interval, gasoline is drained out from the tank at a rate of d(t) = –0.02t 3 + 2.4t 2 + 0.16t cubic feet per hour. (note: the volume v of a cylinder with radius r and height h is given by v = ? r 2 h.) a) determine the volume of gasoline pumped into the tank over the entire 10-hour interval. b) describe all open intervals of t for which the volume of gasoline in the tank is increasing. justify your answer. c) what is the maximum volume of gasoline in the tank over the interval 0 ? t ? 10? justify your answer. d) how fast is the gasoline level in the tank rising at time t = 4 hours? justify your answer.