Thread: Using polar coordinates to find the volume of a bounded solid

1. Using polar coordinates to find the volume of a bounded solid[Solved]

I found the equation of the boundary circle by setting z to 4 in the paraboloid.
Then I did some work to get polar coords:
$x^2+y^2 = 1$
$x^2+y^2 = r^2$
$1-x^2-y^2 = 1-r^2$
Then I set up my integral as such
$\int_0^{2\pi}\int_{0}^{1}(1-r^2)rdrd\theta$
edit: I used the wrong integrand. It should be 4r-4r^3.