# Let S be the intersection of two cylinders or radius r whose axis intersect at angle theta, find the volume… [closed]

I have this problem and I understand most of it, but am having trouble deriving the formula for the side of each rhombus. I think I just can't visualize it well. Can anyone draw a picture that would help me find the side length of the rhombus?

"Let S be the intersection of two cylinders with radius r that intersect at angle theta. Find the volume of S as a function of r and theta.

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## closed as off-topic by GNUSupporter 8964民主女神 地下教會, The Phenotype, Namaste, Shailesh, Parcly TaxelFeb 24 '18 at 2:48

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Consider one of the cylinders, and take a plane parallel to its axis and at distance $0 \le d \le r$ from it.
The intersection of the plane with the cylinder will be two parallel lines, which will be at distance $2\sqrt{r^2-d^2}$ from each other. Can you visualize that ?
Then given two cylinders, whose axes intersect, the two axes will lay on a plane which cuts each cylinder in half. Any plane parallel to that and at distance $d$ from it, will cut each cylinder in a couple of lines as said before.
Those two couples of lines, inclined by the angle $\theta$ are making the rhombus.