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Cylindrical Coordinates and Mathematica

  1. Sep 20, 2008 #1
    Use cylindrical coordinates to draw the paraboloid z=16-x^2-y^2 in Mathematica using ParametricPlot3D.

    so
    z= 16 - x^2 - y^2
    =
    z+x^2+y^2=16
    or
    z+r^2=16
    r=sqrt(16-z)

    thus x=sqrt(16-z)cos(theta) y=sqrt(16-z)sin(theta)
    I know theta goes from 0 to 2pi but how do I find the z range?
    Any help would be appreciated.

    Below is my Mathematica code with a guess for the z min and max:
    ParametricPlot3D[{Sqrt[16 - z] Cos[[Theta]], Sqrt[16 - z] Sin[[Theta]], z}, {[Theta], 0, 2*Pi}, {z, -2, 2},
    ViewPoint -> {6, 3, 2}]

    Thanks
    Stephen
     
  2. jcsd
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