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A Question On Dividing a Sphere

  1. Dec 18, 2013 #1
    I would like to know how to divide a sphere's volume equally into 3 parts, by using two "slices" that are parallel planes. A good example would be cutting a round fruit into 3 equal parts by two slices with a knife. I would like to know the distance (fraction of the diameter) along the diameter where these cuts would be made.
     
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  3. Dec 18, 2013 #2

    Ben Niehoff

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    Then you'll be needing this formula:

    http://en.wikipedia.org/wiki/Spherical_cap

    Set V to 1/3 the volume of a sphere, and solve for h. Looks like a tricky cubic equation; your answer is going to have cube roots in it.
     
  4. Dec 18, 2013 #3

    Simon Bridge

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    Welcome to PF;
    The formula is the way to go ... but this sounds like an exercise for a class.
    That means you may be expected to use a different approach. What's the context?
     
  5. Dec 19, 2013 #4
    It is not a class exercise. It is more of a personal curiosity. I figured it would be a simple solution and couldn't find any after doing some online searching. Thanks
     
  6. Dec 19, 2013 #5

    Simon Bridge

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    OK then - the spherical cap formula is probably fastest.
    The other way is to modify the method for finding the volume of a sphere radius R by integration.

    You could also do it as a volume of rotation of the area between x=s and x=R (-R<s<R) under the circle and above the x axis.

    In each case you'll be finding an equation for s knowing the desired volume.
     
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