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Homework Help: Find volume of solid elliptic paraboloid using polar coordinates

  1. May 22, 2012 #1
    1. The problem statement, all variables and given/known data
    a elliptic paraboloid is x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h. Its apex occurs at the point (0,0,h). Suppose a>=b. Calculate the volume of that part of the paraboloid that lies above the disc x^2+y^2<=b^2.:confused:

    2. The attempt at a solution
    We normally do the questions that ask to find the volume of a cylinder. the polar coordinates are straight, which is x=rcos(), y=rsin();
    but in this question, i don't how to set up the polar coordinates for x and y..:frown:
  2. jcsd
  3. May 22, 2012 #2


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    Gold Member

    Your equation for the elliptic paraboloid appears to be:
    [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}\le \frac{h-z}{h}[/tex]
    Make z the subject of the equation to get the upper limit, as z varies from z = 0. The rest should be easy enough, as you are expected to use cylindrical coordinates to describe the volume.
  4. May 22, 2012 #3
    thanks :)) sharks
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