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

  1. Mar 25, 2010 #1
    Using polar coordinates to find the volume of a bounded solid[Solved]

    zoiy4o.png
    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.
     
    Last edited: Mar 25, 2010
  2. jcsd
  3. Mar 25, 2010 #2

    vela

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    Why are you plugging 1-r2 in as the integrand? What are zupper and zlower?
     
  4. Mar 25, 2010 #3
    Last edited by a moderator: Apr 24, 2017
  5. Mar 25, 2010 #4

    vela

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    Draw a sketch of the volume you're integrating. It'll help you visualize what goes where.
     
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