Your post title was "Determining Volume using double integral". It you want to set it up as a triple integral first then you integrate 1*dz*dx*dy over the volume. The integral of 1*dz is just z. It's the same thing. Now get started.
Not too good I don't think. I'm not too sure what you are trying to draw, but your first step should be to figure out where the two planes intersect. Can you do that? I think that will help you picture the region.