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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- Jul 19th 2005, 01:33 AMcornothPercentage...
A golf ball is packed into a cubical box so that it just fits. What percentage of the box is unfilled?

- Jul 19th 2005, 02:19 AMticbol
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. - Jul 20th 2005, 12:15 AMcornoth
Thanks ticbol!