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Consider two infinite circular cylinders of equal radius whose axes meet in a right angle.

(a) What is the volume of their intersection?

(b) What is the area cut out of one by the other?

How to start this question?

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marked as duplicate by Namaste, Jean Marie, Nosrati, Leucippus, Shailesh Sep 22 '17 at 23:44

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    $\begingroup$ The intersection can be seen as a stack of squares with dimensions that become less once you reach the top/bottom of the cylinders. In other words, there is a relation between the height inside the intersection and the size of a square. $\endgroup$ – imranfat Sep 22 '17 at 22:03
  • $\begingroup$ For the surface area, you can integrate from the midpoint up to the top, and the angle will give you the length of surface intersected at each increment. $\endgroup$ – Joffan Sep 22 '17 at 22:07
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    $\begingroup$ How about you start with equations that describe the cylinders. $\endgroup$ – Doug M Sep 22 '17 at 22:11
  • $\begingroup$ If I had to guess without looking at the solution. I would say that you want to try and intersect the equations of the circles, but also work in an angle as well. $\endgroup$ – Erock Brox Sep 23 '17 at 2:10
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Hint for a: Well,consider that if the axes of the 2 cylinders meet at at a right angle, this means the axes are perpendicular to each other. In other words, it looks like this:

enter image description here

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