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Say I have a function $y=x^2 + 2x + 1$ and I want to plot it over the cross sectional area of a hollow cylinder between $x=1$ and $x=2$ in Mathematica. See the attached example below. How do you go about making figures of this type in Mathematica? enter image description here

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    $\begingroup$ We need three variables to plot such figure, not only two variables. $\endgroup$
    – cvgmt
    Commented Mar 11 at 23:31
  • $\begingroup$ $\theta \in {0,\pi/2}$ $\endgroup$
    – Engineer
    Commented Mar 11 at 23:59
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    $\begingroup$ What are the relation between x,y and θ? $\endgroup$
    – cvgmt
    Commented Mar 12 at 0:08
  • $\begingroup$ Your "equation" makes no sense. $\endgroup$
    – David G. Stork
    Commented Mar 12 at 1:10

2 Answers 2

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Clear["Global`*"];
f[r_, θ_] := r^2 + 2 r + 1;
DensityPlot[
 f[r, θ] // Evaluate, {r, 1, 2}, {θ, 0, π/2}, 
 PlotRange -> All, 
 DisplayFunction -> 
  ReplaceAll[{r_Real, t_Real} :> {r*Cos[t], r*Sin[t]}], 
 ColorFunction -> Hue]

enter image description here

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  • $\begingroup$ Thank you so much! $\endgroup$
    – Engineer
    Commented Mar 18 at 16:10
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Your equation makes no sense. But the closest thing that does make sense is:

RevolutionPlot3D[r^2 + 2 r + 1,
 {r, 1, 2},
 {\[Theta], 0, \[Pi]/2}.
 ColorFunction->"Rainbow"]

enter image description here

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