Re: RevolutionPlot3D Help

*To*: mathgroup at smc.vnet.net*Subject*: [mg119817] Re: RevolutionPlot3D Help*From*: Helen Read <readhpr at gmail.com>*Date*: Fri, 24 Jun 2011 07:44:33 -0400 (EDT)*References*: <itv865$pdh$1@smc.vnet.net>

On 6/23/2011 7:31 AM, tolga wrote: > How can I do revolve a region between two curves around the x axis > with "RevolutionPlot3D" command? It would be helpful if you post a specific example, so that people don't have to guess what you are trying to do. That said, I will make up an example for you. Suppose you wish to revolve the region bounded by y=x^2, y=8-x^2, x=-2, x=2 about the x-axis. To begin, let's define a function for each curve. f[x_] := x^2 g[x_]:=8-x^2 You can easily revolve each curve separately, then combine with Show. plot1=RevolutionPlot3D[f[x], {x, -2, 2}, RevolutionAxis -> x]; plot2 = RevolutionPlot3D[g[x], {x, -2, 2}, RevolutionAxis -> x]; Show[{plot1, plot2}, PlotRange -> Automatic] You can also revolve both curves together at the same time, like this. RevolutionPlot3D[{{f[x]}, {g[x]}}, {x, -2, 2}, RevolutionAxis -> x] Note the extra set of braces { } around each function. If you omit the extra braces, you are in effect telling Mathematica to revolve the parametric curve {f[x],g[x]} instead of two separate functions f[x] and g[x]. Try it: RevolutionPlot3D[{f[x], g[x]}, {x, -2, 2}, RevolutionAxis -> x] Now plot the parametric curve {f[x],g[x]} to see what is being revolved. ParametricPlot[{f[x], g[x]}, {x, -2, 2}, AxesOrigin -> {0, 0}] -- Helen Read University of Vermont