1. The problem statement, all variables and given/known data I am trying to find the volume of three intersecting cylinders that intersect at right angles given that the radius is 5. I have found many sites that state just the answer, but I am after the proof for it showing all of the working. I know how to prove the rule for 2 intersecting cylinders, I can't do it for 3 though. 2. Relevant equations The rule I am after is 8(2-sqrt(2))r^3 or any similar form of that. 3. The attempt at a solution V_3(r,r,r) = 16r^3int_0^(pi/4)int_0^1ssqrt(1-s^2cos^2t)dsdt A site i have found begins solving with that equation, but I have completely no idea where the numbers come from.