Consider a tank in the shape of an inverted circular cone with a height of 20 meters and a top radius of 4 meters. Using 9.8m/s^2 for the acceleration due to gravity and 1,000kg/m^3 as the density of water. Set up the integral that represents the work required to pump the water out of the tank if the tank is full of water but you just want to pump half the water out of the tank (down to a depth of 10 meters) over the top of the tank if: a. the tank is full of water and it is being pumped out of a 1-meter long vertical spout at the top of the tank.
b. the tank is half full of water and it is being pumped out of a 0.5-meter long vertical spout at the top of the tank.
c. the tank is full of water and it is being pumped out over the top of the tank.
d. the tank is full of water but you just want to pump half the water out of the tank out over the top of the tank.