# How to calculate the volume of intersection of two cylinders which have radius $r$ and $R$ $(r\le R)?$

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?

• For the general case, you can see this question. For a particular case, you can see this answer. – Watson Feb 15 '16 at 22:47
• 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
• 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 at 11:51