# How can I plot a surface in cylindrical coordinates? [closed]

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

Please tell me how to do it in Mathematica.

## closed as off-topic by Henrik Schumacher, Coolwater, bbgodfrey, Pinti, SumitNov 22 '18 at 19:50

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• ContourPlot3D? – Henrik Schumacher Nov 19 '18 at 17:05
• @Henrik Schumacher How would you write the function? – Brandon Nov 19 '18 at 18:17
• 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

## 1 Answer

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]