The maximum volume of water. We are a group of math enthusiasts and we design and present our mathematical problems to societies. This week I designed this problem and I thought it might be interesting to share it with you here. If you think sharing such problems are not appropriate for this site, then I can remove it.
Here is the problem:- A spherical glass is resting on its side on a table. What is the maximum volume of water it can hold in that position?
We ignore the thickness of the glass edges.
The picture is designed and rendered in $PovRay$.


Here is my solution to the maximum volume of water in a glass. The important step in this solution is to find the angle of rotation of the glass when it is resting on the table. 

