The problem to find the volume enclosed by intersection of three cylinders had become too tough for me, but then I found this and benorin's answer to this thread was marvelous. It was very clear and simple.
I have few doubts regarding that reply, I request you kindly to help me.

1. How to get that first octant model? I mean it's hard to visualize.

2. Please explain the second figure. Actually, I'm getting the problem of which color represents which cylinder $\displaystyle x^2 +y^2 =1$, $\displaystyle y^2 +z^2 =1$, $\displaystyle x^2 +z^2 =1$ and how he has cropped it?

3. Please explain the bounds of $\displaystyle \theta$, I means please elaborate how $\displaystyle 0 \leq \theta \leq \pi/4 $ ?

4. The symmetry is always a problem to me. Please explain how that part represents the $\displaystyle \frac{1} {16} $ of the volume.

Thank you. Any help will be much appreciated. I hope that experienced people over here will understand my doubt and will help to the fullest.

I have been through those Wolfram's solution and Wikipedia's solution for this problem but I couldn't convince myself to accept their solution