Consider a sphere shaped tank. Suppose it has radius 2. It is filled 2/3 of the way with slime. What is the depth of the slime at its deepest point (i.e. what is the height of the slime in the tank when the tank is 2/3 of the way full). Use calculus methods.
Next, compute the work to pump the slime out the top of tank that is 2/3 full, using the density of slime as 1000 kg/m^3
I know you do 4/3 pi r^3 for the volume of the tank, and so you can find the volume of 2/3 the tank, but how about the height?