       Re: RevolutionPlot3D Help

• To: mathgroup at smc.vnet.net
• Subject: [mg119817] Re: RevolutionPlot3D Help
• 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}]

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