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?


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

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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