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Help extending volumes of revolution to fourth dimension

  1. Feb 19, 2012 #1
    I am currently learning about volumes of revolution in calulus, and have looked ahead to surfaces of revolution as well. I want to try and extend this concept to revolving 3d functions over the x-axis into the fourth dimension. I found this thread:
    and saw how to find the content of a 3-ball (5th post).

    I attemted to use this idea to find the content of the revolution about the x-axis of the revolution about the x-axis of 4-x2 but I couldn't quite puzzle through the method described in the above thread for anything other than spheres. The closest I came was the surface area of the solid of revolution, and realizing that I need to describe the circumference of the 3d solid of revolution with respect to the radius and/or height (for a sphere of radius 1 it would be 2[itex]\pi[/itex]ssin(r))

    Can anyone point me in the right direction, or does this seem way too far past a Calculus DC student in highschool? (and if so I'm still really interested in how this would work)
  2. jcsd
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