Use cylindrical coordinates to draw the paraboloid z=16-x^2-y^2 in Mathematica using ParametricPlot3D.(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Cylindrical Coordinates and Mathematica

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