Just recently I was posed with the following interesting question:
Say you took a sphere with an arbitrary, constant radius "$R$" and dropped it into Gabriel's Horn. Then you filled the horn perfectly with water such that the sphere acts like a plug and stops water from passing. What is the volume of the water that was poured into the horn?
The primary trouble is determining where it is that the sphere gets lodged in the horn, and determining what percentage of the sphere is above the point at which it is lodged. I thought it would be interesting to see what sort of solutions there were.