Calculating Volume of Intersection for 3 Balls with Different Centers

[mccoy1]

Homework Statement

If i have 3 balls of radii =2 and centres =(1,0,0),(0,1,0) and (0,0,1). Find the volume of the intersection of the three balls.

Homework Equations

The Attempt at a Solution

The only method i know only works when the first ball has a centre at (0,0,0) and the second has the centre at x-xis. But these three balls have their centres at each axis. What can I do? Thank you guys.

 

[micromass]

Hi mccoy1!

Maybe you can translate and rotate the space a bit such that the three balls do satisfy your conditions. And since translations and rotations preserve voluma, we can do this.

So, first, try to translate the space such that one vector ends up in (0,0,0).

 

[mccoy1]

Hi mccoy1!



So, first, try to translate the space such that one vector ends up in (0,0,0).

It makes sense, but how do I do just that? I haven't learn that yet to be honest. I'll google it in a meanwhile.
Thanks for the tip.