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Math Help - How to find the volume of a "corner" of a cylinder?

  1. #1
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    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)?
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  2. #2
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    I don't see it. Can you post a picture?
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  3. #3
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    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?
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  4. #4
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    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.
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