There is a formula in order to find out the Volume of a cylinder, if there were to be some amount of liquid placed inside that cylinder, we could calculate the volume by replacing the height of the cylinder with the height of the liquid. What I would like to find out is how to find out the volume of the liquid if the cylinder were to be tilted anywhere from 0 to 90 degrees. and for any amount of liquid, since that also determines the shape of the liquid inside.
I assume that it might involve triple integration, but I am not sure. also it might be able to solve this using Simpson's rule, but i do not know how that works.
any help would be greatly appreciated.