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Sphere in a cone (ball in a wine glass)

  1. May 14, 2006 #1


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    sphere in a cone (ball in a martini glass)

    A problem a friend mentioned to me years ago.

    You have a cone with height H and angle A. What is the radius R of a sphere that when placed in the cone, displaces the most volume?

    One suggestion was to reduce this to a two dimentional case.
    Last edited: May 14, 2006
  2. jcsd
  3. May 14, 2006 #2


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    Yeah, rotational symmetry would allow reduction to the 2-d case; so, set it up: what's the equation of a cone of angle A? the equation of the circle of radius R circumscribed therein? do the integral, get it in terms of R, differentiate w.r.t. R and set equal to 0.
  4. May 14, 2006 #3


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    Correction: ball in a martini glass.

    Glad I could help.
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