http://i.imgur.com/WMWUp1D.jpg?1

The sphere problem asks you to find the volume of the region bounded by the plane z=1/2 and a ball with radius 1 centered at the origin using spherical coordinates. I'm not even expected to evaluate it, just figure out the bounds correctly. I guess the major work was finding the phi value of pi/3 and the rho value of 1/2sec(phi)

Cylinder Work

http://i.imgur.com/iysXAvR.jpg?1

The cylinder problem asks to find the smaller volume bounded by the cylinder of radius 4, the plane x=sqrt(8) and the plane z=100-3y. It was a little bit more complicated at least to me, I had to calculate where x=sqrt(8) intersected with the xy trace of the cylinder, define the height in cylindrical and as I'm writing this I realize I screwed up my R bounds. In order to get the minor segment of the xy trace (the smaller segment) it should be r=sqrt(8)sec(theta)..4.

I consider this post already helpful since I've found a mistake just from writing it but I would definitely appreciate someone else looking at my work briefly and make sure I'm doing these right. They evaluate out reasonably with Wolfram, so I suspect I'm at least close.