# Mathematica and volumes of rotated solids

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• Sep 25th 2008, 03:13 PM
redman223
Mathematica and volumes of rotated solids
I have no clue how to do these types of problems on mathematica and I have no clue how to even search mathematica for help.

What do I need to do to find out how to solve these problems in mathematica?

I tried google to no avail, I guess I don't know what to look for.
• Sep 25th 2008, 03:36 PM
shawsend
Try RevolutionPlot3D:

RevolutionPlot3D[x^2, {x, 0, 1}]

That would simply rotate the half-parabola around the z-axis. Need to work with the help-function: Type that above into Mathematica, put cursor over it, press F1 and you'll get help as well as other related functions. The help is much improved in ver 6.
• Sep 25th 2008, 05:04 PM
redman223
You mean it will revolve around the x-axis right?

I heard that mathematica has lots of examples, but I am having trouble finding them. For example, what would I type in order to find the volume of the area enclosed by y=x^2 y=2x x=2 x=4 around the y-axis? (I just made those numbers up right now, hopefully they will work, otherwise a similar example that works would be awesome)
• Sep 26th 2008, 04:23 AM
shawsend
Ok, y-axis. You have to build them up although there may be an easier way to do that. Here's what I came up with. The second is a cross-section of the volume of revolution.

Code:

cyl = ParametricPlot3D[{4*Cos[t], 4*Sin[t],
z}, {t, 0, 2*Pi}, {z, 8, 16}]
p1 = RevolutionPlot3D[{x^2}, {x, 2, 4},
BoxRatios -> {1, 1, 1}, PlotStyle -> Red]
p2 = RevolutionPlot3D[{2*x}, {x, 2, 4},
BoxRatios -> {1, 1/4, 1},
PlotStyle -> Blue]
fig1 = Show[{p1, p2, cyl}]
fig2 = Show[{p1, p2, cyl}, PlotRange ->
{{-4, 4}, {0, 4}, {0, 16}}]
GraphicsArray[{{fig1, fig2}}]