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What's the area of this volume?

  1. Jul 24, 2004 #1
    Consider a 3d coordinate system with axis x,y and z.

    We are given a circle on the x-z plane with function [tex]z^2 + (x-a)^2 = a^2[/tex]. We rotate this circle 90 degrees around the z-axis. What's the volume of the resulting surface?
  2. jcsd
  3. Jul 24, 2004 #2


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    Well, shouldn't that be a quarter of a torus?
    I'll opt for that and say:

    The area function for a given angle measured relative to the x-axis (and with the origin as the pole) is [tex]f(\theta)=\pi{a}^{2}[/tex]

    By Cavalieri's principle, we have:
    Last edited: Jul 24, 2004
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