# Trying to plot a region in 3D

I'm trying to plot the region enclosed by the curves

$$\begin{cases}y^2=x\\y^2=4-x\\z=0\\z=3\end{cases}$$

using the command RegionPlot (I'm not sure if Plot3D or ParametricPlot3D are more appropriate). The desired region looks like a cylinder but with a parabolic-intersection cross section: Now I'm running the command

RegionPlot3D[y^2 < x && y^2 < 4 - x && z > 0 && z < 3, {x, 0, 4}, {y, -3,  3}, {z, -3, 3}]


But I get the following weird-looking region instead. Can anyone help me plot the desired region? and is there perhaps a better/more suitable command for such a thing?

• Try contourRegionPlot3D[] from here. – J. M. will be back soon Jan 22 '17 at 11:00
• @J.M. - it sorted it! Cheers – Luke Collins Jan 22 '17 at 11:04

Increasing the number of PlotPoints results in a more satisfactory plot.

RegionPlot3D[y^2 < x && y^2 < 4 - x && z > 0 && z < 3,
{x, 0, 4},
{y, -3, 3},
{z, -3, 3},
PlotPoints -> 100
] In version 11 just simply confining argument to x,y dependence yields a satisfactory result:

 RegionPlot3D[y^2 < x && y^2 < 4 - x, {x, 0, 4}, {y, -3, 3}, {z, 0, 3},
Mesh -> None, PlotPoints -> 40] 