# How do I plot $x^2+y^2=1$ in 3D?

How would I plot $x^2+y^2=1$ in 3D (it would form a cylinder)? Since there is no $z$ in the equation, I can't solve for it and use Plot3D. Or can I just put the equation into Plot3D? I am very new to Mathematica.

How about a 3D contour plot.

ContourPlot3D[x^2 + y^2 == 1, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]

• Oh, great! Thanks! Sep 16, 2012 at 22:52
• No problem! Have fun Ben. Sep 16, 2012 at 22:54

Although Mark's answer is the "natural" one, here are other options just for completeness:

Use Plot3D, after performing a rotation:

Plot3D[{1, -1} Sqrt[1 - x x], {x, -1, 1}, {y, -1, 1},  AspectRatio -> 1]


Use ParametricPlot3D[]:

ParametricPlot3D[{{1, -1, 1} #, {1, 1, 1} #} &@{x, Sqrt[1 - x x], z}, {x, -1, 1}, {z, 0, 1}]


Use RevolutionPlot3D[] after realizing for example that in the semi/plane {y==0, x>0} x takes only the value 1 and z takes any value (freely):

RevolutionPlot3D[{1, t}, {t, 0, 1}]


• Yet another possibility: ParametricPlot3D[RotationTransform[θ, {0, 0, 1}][{1, 0, r}] // Evaluate, {r, 0, 1}, {θ, 0, 2 π}] Sep 17, 2012 at 11:00
• Man, thanks so much for this. This is great. Sep 19, 2012 at 2:00