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I have a problem concerning a cylinder, cut by an arbitrary plane which is perpendicular to an axis, z.

I know dz, the distance from centre of the cylinder to the plane. I know all dimensions of the cylinder. I know theta, the angle of rotation from the axis z.

My poor drawing

How do I calculate the volume of the cylinder above the plane? Is it possible? I've tried some trigonometry to get an integral based on the changing size of a circle segment... but it's getting very convoluted.

Michael McFarlane
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  • I believe the shape you're looking at (the part of the cylinder above the solid horizontal line in your sketch) is called an ungula. You might find this post helpful. – user170231 May 05 '23 at 16:37
  • Thanks for this! It looks like the solution for an ungula assumes that it meets the centre of the cylinder base, which might not be the case here; but, I'll look to see if it gets me an answer. Thanks again. – Michael McFarlane May 05 '23 at 17:12
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    You're answer led me to here: https://mathworld.wolfram.com/CylindricalWedge.html, which I think gives me what I'm after. Thanks once again – Michael McFarlane May 05 '23 at 17:29

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