Water is pumped into a spherical tank of radius 5 ft from a source located 2 ft below a hole at the bottom. Density of water=62.4. Find the work F(h) to fill the tank to a height h from the bottom of the tank.
I know F(0)=0 and F(10)=228708 by computing the work to fill the tank. It is clearly going to be a continuous function and it fills faster in the middle, the domain will be 0<=h<=10, but how do I find the equation for this? I know I can still use the same geometry I did for finding F(10), with center at the center of the sphere, but I am confused how to get a function out of this.