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Cylinder sketch in 3-d?

  1. Sep 24, 2008 #1
    1. The problem statement, all variables and given/known data

    I have to find the volume of the region bounded by a cone and cylinder. (double integral style!)
    I usually start off with a sketch, but I can't seem to figure out what this one quadratic surface looks like...

    It's a cylinder (in 3-dimensional plane): x2+y2=2ay

    3. The attempt at a solution

    I know that the equation of a cylinder is just x^2+y^2=a in 3-d. I also know the equations of a hyperbolic, oblique, and parabolic cylinder......but I don't think this is one of those.
    Anyone willing to help me out, or at least point me in some sort of direction!
  2. jcsd
  3. Sep 24, 2008 #2


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    Homework Helper
    Gold Member

    Try rewriting the equation into standard form:

    [tex] \Rightarrow x^2+y^2-2ay=0[/tex]
    [tex] \Rightarrow x^2+(y-a)^2-a^2=0[/tex]
    [tex] \Rightarrow x^2+(y-a)^2=a^2[/tex]

    Which is the equation of a cylinder of radius a centered at (0,a) running parallel to the z-axis.
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