Hello, ratedmichael!
A sphere of radius 3 passes through the center of a sphere of radius 1.
Find the volume of the region inside the sphere of radius 3 and outside the sphere of radius 1. [size=3] Code:
3
* * *
*  *
*  : *
*  : *o
 :o o
*  o * o
  *      +    o  *  o  
3*  2o *3 o
 :o o
*  : *o
*  : *
*  *
* * *

We have a crosssection of the spheres.
We will revolve the appropriate regions about the xaxis.
The large circle has equation: .
The small circle has equation: .
On , we revolve about the xaxis:
. .
The circle intersect at
On , we find the difference of the volumes.
. .
Got it?