Water to fill a swimming pool (calc 3)

Question

A circular swimming pool with a diameter of 20 meters has a plane floor that is horizontal going from north to south, but at constant incline going from east to west, with the lowest point 7 meters below the rim of the pool and the highest point of the floor at 5 meters from the rim of the pool. Determine the amount of water needed to fill the pool to its rim.

I really have no idea where to start on this problem, I can't seem to picture it in my head. I imagine I am going to have to use cylindrical or spherical coordinates in setting up a integral but I don't know where to start.

Thanks in advance

Answer 1

Here is a depiction of the volume of interest.

Answer 2

Without integration and by simple geometry: $$V=V_1+V_2=\pi R^2h_1+\frac12\cdot \pi R^2h_2=\pi \cdot 10^2\cdot 5+\frac12\cdot \pi \cdot 10^2\cdot 2=600\pi.$$