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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1For the general case, you can see this question. For a particular case, you can see this answer. – Watson Feb 15 '16 at 22:47
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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. – Martín-Blas Pérez Pinilla Feb 15 '16 at 23:02
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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. – Lee David Chung Lin Jan 22 '19 at 11:51