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I want to plot the volume of a cylinder between a cone and the plane XY

The equation of the cone is $z$ $=$ $\sqrt{x^2 + y^2}$ and the cylinder equation $y^2 - 2y + x^2 = 0 $

I am using the following code to plot the graphs:

      p3 =  Plot3D[{Sqrt[x^2 + y^2], 0}, {x, -2, 6}, {y, -5, 5}]
      p4 = ContourPlot3D[{y^2 - 2 y + x^2 == 0}, {x, -5, 5}, {y, -5, 
       5}, {z, -5, 5}]
      show [p3,p4]

And I get the following

enter image description here

How can I plot only the volume of the cylinder between the cone and the plane XY

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    – Michael E2
    Apr 28, 2015 at 23:34

2 Answers 2

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You can use the RegionFunction option on ContourPlot3D to only plot the cylinder above the plane and below the cone.

ContourPlot3D[{y^2 - 2 y + x^2 == 0}, {x, -5, 5}, {y, -5, 5}, {z, -5, 5},
  RegionFunction -> Function[{x, y, z}, 0 <= z <= Sqrt[x^2 + y^2]]]

Edit

The above is correct, but the plot will look better if it is focused on the relevant region.

ContourPlot3D[
  y^2 - 2 y + x^2 == 0, {x, -1, 1}, {y, 0, 2}, {z, 0, 2.5}, 
  RegionFunction -> Function[{x, y, z}, 0 <= z <= Sqrt[x^2 + y^2]],
  BoxRatios -> {2, 2, 2.5}]

plot

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  • $\begingroup$ I edited your answer to show how the plot can be focused on the relevant region by making a more suitable choice of plot range. $\endgroup$
    – m_goldberg
    Apr 29, 2015 at 2:59
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The solution provided by @Edmund does not show the top (curved) face of the region. The following does:

RegionPlot3D[z < Sqrt[x^2 + y^2 ] && y^2 - 2 y + x^2 < 0 && z > 0,
 {x, -1.5, 1.5}, {y, -.5, 2}, {z, 0, 2},
 PlotPoints -> 100]

enter image description here

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