The volume inside the cylinder, , is easy:
But that misses the volume, above the cone, that lies in the annulus between the two circles, and . To do that you will need to separate it into four integrals:
The first with x from -2 to , y from to , z from to
The second with x from to , y from to , z from to
The third with x from to , y from to ,z from to
The fourth with x from to , y from to ,z from to
That might make more sense to you if you draw the circles in the xy-plane and mark out each of the five regions above
To actually find the volume, it would be much easier to use spherical coordinates. In spherical coordinates, goes from 1 to 2, goes from 0 to , and goes from 0 to .