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Homework Help: Volume under a paraboloid and above a disk

  1. Nov 15, 2009 #1
    Ok its a simple question really... say that I have to find the volume (using polar coordinates) of the solid under the paraboloid z=x^2+y^2 and above the disk x^2+y^2≤9. My approach would be to find the z value of where the cylinder and paraboloid intersect. Then find the volume of the paraboloid using the value of the plane where it intersects, then subtract it from the volume of the cylinder, this seems right to me. I'm getting z=18 for the point where the cylinder and paraboloid intercept, is this right? For some reason my gut is telling me that its 9 not 18. I simply plugged in the radius of the circle into the paraboloid formula
  2. jcsd
  3. Nov 15, 2009 #2
    After calculating this I got 40.5*pi, is this correct? is there a way that I can check this?
  4. Nov 15, 2009 #3


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    The only way to check it is to try and find another way to do it and see if you get the same thing. I did it using polar coordinates (which is pretty easy) and got 81*pi/2.
  5. Nov 15, 2009 #4
    thanks I also got the same as you, im prety sure we're both right. Thanks again
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