Integrating in polar coordinates (volume)

[rhyno89]

Homework Statement

The solid bounded by the parabolids z = 3x^2 + 3y^2 -7 and z = -x^2 -y^2 + 9

Homework Equations

The Attempt at a Solution

Ok so i set the two z equations into polar form and came up with 3r^2 = 7 and r^2 = 9
I thought that r went from (7/3) ^(1/2) to 3 and that theta went from 0 to 2pi.
I figured the equation to integrate was -4r^2 + 16. (Outer bounds -inner bounds) Anyway, the answer the book gives is different than the two different ways I tried. Just need help setting up the integral...thanks

 

[Dr.D]

This is a 3-D problem; you were given z coordinate values in each case. Work with those.