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Volume, rotation around axis

  1. Oct 8, 2009 #1
    Unfortunately my geometry is a little rusty: if I have an area A(x,y), and rotate it around axis z (yielding a symmetrical, circular body), what is the algorithm to calculate volume?

    Or am I remembering incorrectly, and the algorithms were for very specific shapes?

    E.g. a circular cylinder with a cone on top; viewed from the side it has a cross-sectional area A, and rotated around axis z you get volume.
     
    Last edited: Oct 8, 2009
  2. jcsd
  3. Oct 8, 2009 #2

    HallsofIvy

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    The only "algorithm" is "Heron's formula": the volume of a solid of revolution, that is, a two-dimensional region rotated around an axis, is the area of the region times the distance the center of the region moves. That, in turn, is the area times 2 [itex]\pi[/itex] times the distance from the center to the axis of rotation.

    Of course, for a general region, finding the center requires integration. So you might as well do it as an integral to start with.
     
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