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.
The rule I am after is 8(2-sqrt(2))r^3 or any similar form of that.
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.