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

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:
[tex]x^2+y^2 = 1[/tex]
[tex]x^2+y^2 = r^2[/tex]
[tex]1-x^2-y^2 = 1-r^2[/tex]
Then I set up my integral as such
[tex]\int_0^{2\pi}\int_{0}^{1}(1-r^2)rdrd\theta[/tex]
After the double integration, I get pi/2.

edit: It should be 4r-4r³ as the integrand.

 

I think that's the root of my problem. I found a http://answers.yahoo.com/question/index?qid=20080327174835AA36kOs" that's similar, but it doesn't show the work to get the integrand.