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Math Help - Mathematica and volumes of rotated solids

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    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)
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  4. #4
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    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}}]
    Attached Thumbnails Attached Thumbnails Mathematica and volumes of rotated solids-volrev3.jpg  
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