Water in a cylinder of height 10 ft and radius 4 ft is to be pumped out. Find the work required if
(a) The tank is full of water and the water is to be pumped over the top of the tank.
(b) The tank is full of water and the water must be pumped to a height 5 ft above the top of the tank.
(c) The depth of water in the tank is 8 ft and the water must be pumped over the top of the tank.
W = F * D
Density of water = 62.4 lb/ft^3 (weight)
The Attempt at a Solution
I know that I have to slice up the cylinder into arbitrarily small cylinders and find the work for each cylinder. I'm not sure how to slice it, and the thing that really confuses me is how the limits of integration change with each problem.