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## Homework Statement

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.

## Homework Equations

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.