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paraboloid

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**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-4r

^{3}as the integrand.

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