[SOLVED] Cylindrical Coordinate Volume Integration

9. Use polar coordinates to compute the volume of the region defined by 4 - x^2 - y^2 less or equal to z less than or equal to 10 - 4x^2 - 4y^2.

answer in book: 6pi

my answer: 2pi

http://img149.imageshack.us/img149/3562/31957521.jpg

I got the root of 2 by setting the equations that bound z equal to eachother. It resulted in an equation for a circle equal to two. And to get the area of a circle, you have to do all 360 degrees, so I used 2pi. What's going wrong here?