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Math Help - Percentage...

  1. #1
    Junior Member
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    Percentage...

    A golf ball is packed into a cubical box so that it just fits. What percentage of the box is unfilled?
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  2. #2
    MHF Contributor
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    Golf balls have dimples so the diameter of a golf ball is not constant, yet, still, since it is not mentioned, we assume that the golf ball has a constant diameter "d", and so the inside of the box is a cube that is "d" per side.

    Golf ball is a sphere
    Diameter = d
    Radius = r
    Volume, Vg = (4/3)pi r^3

    Inside of box is a cube of d per side
    Side = d = 2r
    Volume, Vb = d^3 = (2r)^3 = 8r^3

    Unfilled space inside of box, Vu = Vb -Vg
    Percentage of Vu relative to Vb is
    = Vu / Vb
    = (Vb -Vg) / Vb
    = (8r^3 -(4/3)pi r^3) / (8r^3)
    The r^3 cancels out,
    = (8 -4pi/3) / 8
    = 0.4764
    In percentage,
    = 47.64 % ------answer.
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  3. #3
    Junior Member
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    Thanks ticbol!
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