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The cylinders have their axis meet at right angle. I try to use integral to derive the equation but I have a hard time visualizing the edge of intersection. Could someone help?

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    $\begingroup$ For the general case, you can see this question. For a particular case, you can see this answer. $\endgroup$ – Watson Feb 15 '16 at 22:47
  • $\begingroup$ Idea that maybe will work: write the big cylinder as $z = \pm f(x,y)$. The volume will be 2(integral of $f$ on the domain $x^2+y^2\le r$). Try first in cilyndrical coordinates. $\endgroup$ – Martín-Blas Pérez Pinilla Feb 15 '16 at 23:02
  • $\begingroup$ Aside from the existing links, this comment is to link this post as one of the (abstract) duplicates to the current choice of mother/target post. $\endgroup$ – Lee David Chung Lin Jan 22 at 11:51

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