# Thread: How to find the volume of a "corner" of a cylinder?

1. ## How to find the volume of a "corner" of a cylinder?

Imagine looking at a cylinder side-on. Now cut off a "corner" of the cylinder from the top such that there is still some flat surface on the top. How do you calculate the volume of the bit you cut off, as a function of the cylinder radius r, cut angle theta (where 0 is horizontal), and cut position x (some position across the top of the cylinder)?

2. I don't see it. Can you post a picture?

3. I actually found a "solution" here, the picture at the top of this page shows in blue the volume I want to calculate.

Unfortunately I don't really understand the solution there, is there no simple algebraic version or must it involve integrals?

4. There is a reason why difficult problems are difficult. There is no easy solution.

I didn't look at it very long, but I would guess some calculus would be the easiest solution. Having said that, I would expect Archimedes to have figured it out.