How can I plot a surface in cylindrical coordinates?

Question

The surface I want to plot is $z^2 + r^2 = 25\, \theta$.

Please tell me how to do it in Mathematica.

That depends. What is $z$, $r$, $\theta$? I guess you try to express an equation in cylindrical coordinates... but who knows? — Henrik Schumacher, Nov 19 '18 at 18:20
See, for instance, the first example in TransformedField. You can then apply ContourPlot3D[Evaluate@TransformedField[..],...] — Michael E2, Nov 22 '18 at 19:50

score 2 · Answer 1 · answered Nov 19 '18 at 19:33

Brandon: You could modify the example given in: How do I make a 3DPlot using cylindrical coordinates? as follows:

cylinderPlot3D[f_, {rMin_, rMax_}, {\[Theta]Min_, \[Theta]Max_},opts___] :=ParametricPlot3D[{r Cos[\[Theta]], r Sin[\[Theta]],f[r, \[Theta]]}, {r, rMin, rMax}, {\[Theta], \[Theta]Min, \[Theta]Max}, opts]

g[r_, \[Theta]_] := Sqrt[25 \[Theta] - r^2];

cylinderPlot3D[g, {0, 1}, {0, 2 Pi}, Mesh -> None, Boxed -> True]

How can I plot a surface in cylindrical coordinates?

1 Answers1