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.

enter image description here


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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, The Phenotype, Namaste, Shailesh, Parcly Taxel
If this question can be reworded to fit the rules in the help center, please edit the question.


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.


Not the answer you're looking for? Browse other questions tagged or ask your own question.