Triple integral to find the volume

[edough]

Homework Statement

use a triple integral to find the volume of the region that is common to the interiors of z^2 +y^2 + z^2 = 1 and x^2 + z^2 = 1

Homework Equations

Would I just calculate the are of the disc? I set up a triple integral as inte [0 to 1] 2nd inte [0 to sqrt(1-z^2)] 3rd inte [0 to 0] dy dx dz
That doesn't really work though since after the first integration it would just be 0 (??)
How would you set up this triple integral? (I might just not be understanding what the region is??)

 

[Mark44]

This isn't a double integral, so the region of integration isn't a disk or other two-dimensional object. The region of integration is the three-dimensional space that is "common to the interiors of z^2 +y^2 + z^2 = 1 and x^2 + z^2 = 1."