Volume of a region between two spheres?

[lax1113]

Homework Statement

Find the volume of a sphere bounded above by the sphere x^2 + y^2 + z^2 = 1 and below by the sphere X^2 + y^2 + (z-1)^2 = 1.

Homework Equations

The Attempt at a Solution

In class we have been doing double integrals with rectangular and polar, but I kinda feel like this would be a triple integral since we are going to have to consider dz dy and dx. I know sometimes we can substitute for one (for example we have done the intersection of a plane and a quadric surface such as a paraboloid) but I am really not sure how I would go about starting this.
Also, we have yet to cover integrals involving spherical coordinates yet, so I don't think that is what he is expecting us to use.

I apologize for not having a real attempt at the solution, but at the moment I am just looking for a step in the right direction so that I can hopefully get something going.

Thanks,
Ben

 

[LCKurtz]

Find the equation of the intersection of the two spheres (subtract the equations to get z). That will give you the boundary of the xy domain. Then just use a double integral with polar coordinates, taking care which is the upper and lower surface.

 

[lax1113]

LC,
Thanks a lot. After that it was actually pretty simple. I just couldn't really think of how to get to that point, greatly appreciate the hint.