# How to graph in Cylindrical coordinates in 3D

I need help figuring out how to plot in cylindrical coordinates. I read that CylindricalPlot3D was replaced with RevolutionPlot3D. Here is my function:

Integrate[ r^3*(Cos[ θ])^2, { θ, 0, 2 π}, {r, 0, 1}, {z, 0, 2 r}]

(2 π)/5


when I try RevolutionPlot3D I get:

RevolutionPlot3D[ r^3*(Cos[θ])^2, { θ, 0, 2 π}, {r, 0, 1}, {z, 0, 2 r}]

RevolutionPlot3D::nonopt: Options expected (instead of {z,0,2 r}) beyond position 3
in RevolutionPlot3D[r^3 Cos[θ]^2,{ θ,0,2 π},{r,0,1},{z,0,2 r}].
An option must be a rule or a list of rules. >>

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@Kuba I wonder if people take the time to reformat code would it be too much extra to replace i -> I? Sorry for nitpicking, but you inter-edited my edit which I discarded :) Also \[Theta] to θ. – István Zachar Dec 6 '13 at 7:56
i'm sorry i don't know what code reformat i was supposed to use. i'm trying to plot this triple integral volume. – user10977 Dec 6 '13 at 7:59
@IstvánZachar you are right, I was not paying attention. About greek letters, I replace them only when I'm on pc with the addon for it, now I'm not :) – Kuba Dec 6 '13 at 8:00
@user10977, what are you trying to visualise, the function r^3 Cos[θ]^2 or the volume over which you have integrated it? – Simon Woods Dec 6 '13 at 9:40
Your syntax is not valid for CylindricalPlot3D either. Do you have existing code you are trying to run? If not, why the reference to CylindricalPlot3D? – Mr.Wizard Dec 6 '13 at 17:33

RevolutionPlot3D accepts only a maximum of two variables for iteration in the form RevolutionPlot3D[f, {t, ...}, {θ, ...}]. Nevertheless, one can manipulate the third:

Manipulate[RevolutionPlot3D[r^3*(Cos[θ])^2, {θ, 0, 2 π}, {z, 0, 2 r},
AxesLabel -> {"X", "Y", "Z"}, SphericalRegion -> True, Mesh -> False,
PlotRange -> {{-7, 7}, {-7, 7}, {-2, 2}}, BoxRatios -> {1, 1, .5}],
{{r, π/2}, 0.001, π}]


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thank you very much for the response but that's not what it is supposed to look like. it needs to be the solid volume solid that lies within the cylinder x^2+y^2=1, above the plain z=0 ,and below the cone z^2=4x^2+4y^2. i converted to cylindrical coordinates (z,r,theta) – user10977 Dec 6 '13 at 8:51
@user10977 So you want this RegionPlot3D[x^2 + y^2 < 1 && z^2 < 4 x^2 + 4 y^2, {x, -1, 1}, {y, -1, 1}, {z, 0, 2}, PlotPoints -> 40, MaxRecursion -> 3, PlotRange -> All, Mesh -> None, PlotStyle -> Opacity@.3] but done with RevolutionPlot3D? – István Zachar Dec 6 '13 at 12:30
Yes yes thank you that is exactly the shape i need you are the best. It does not need to be with RevolutionPlot3D. I should have explained myself more clearly. I'm looking to create a graph with that solid/volume that i can manipulate the variables just like this example: demonstrations.wolfram.com/data/001571/0007/… – user10977 Dec 7 '13 at 0:25
here is the page it comes from demonstrations.wolfram.com/ExploringCylindricalCoordinates – user10977 Dec 7 '13 at 0:35