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Maximize volume of a cone

  1. Sep 27, 2004 #1
    A conical cup is to be made by joining the edges OA, OB of the sector of a circle of radius 8cm. What angle @ gives the cup of maximum volume?

    I'm having trouble solving this question. This is what I have done so far

    we know V=pi*r^2*h/3

    r is given, so we need to put h in terms of @.
    now by similar triangles we can take another slice, and compare
    r/h=R/(h-1).... (h-1) is just the height of the triangle below the new slice
    solving for h I get h=1/(1-R/r) now i'm unsure of what to do now, and how to get @ into the equation.

    Anyways please let me know if i'm doing this question completely wrong or what not. Thanks for all your help
  2. jcsd
  3. Sep 27, 2004 #2


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    r is not given! You're given the radius of the sector of the circle but that is not the same as the radius of the cone.
  4. Sep 27, 2004 #3
    a picture would help
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