A golf ball is packed into a cubical box so that it just fits. What percentage of the box is unfilled?
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.