In this video, I set up the double integral representing the volume between the two surfaces. My software only allows me to create videos that are one hour long or less, and I ended up running out of time while evaluating this integral! I tried to rush at the end, and realized that I had run out of time.
The volume turns out to be pi/2. The integration is much easier in polar coordinates. I'll show you how to evaluate the integral by switching to polar coordinates in another video.