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I'm trying to graph the revolution of the area between two functions about an axis, but I'm new to Mathematica, and not sure how to proceed. My area is defined by

Plot[{x^2,x},{x,-5,5}, Filling -> {1->{2}}]

Just to clarify, the figure I'm looking is 3-dimensional, and could loosely be called a toroid.

How could I model this in 3D?

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  • $\begingroup$ closely related $\endgroup$ – Kuba Jan 13 '14 at 16:13
  • $\begingroup$ @Kuba somewhat related; I'm just trying to graph the toroid (and not the actual curves), not calculate the area. $\endgroup$ – Jules Jan 13 '14 at 16:17
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Show[Plot3D[{(x x + y y), -Sqrt[(x x + y y)]}, {x, -5, 5}, {y, -5, 5},
            RegionFunction -> (#1^2 + #2^2 < 25 &)], 
     RevolutionPlot3D[{5, t}, {t, -5, 25}, Mesh -> None, 
                      PlotStyle -> Directive[Orange, Opacity[.5]]]]

Mathematica graphics

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