Ratio between the volume of a sphere and a cube

Question

A round holiday ornament with radius r is to be packaged in a cubical box so that all sides touch the ornament. what is the ratio of volume of the sphere to volume of the cube?

Volume[sphere]= (4/3rds)(pie)(radius) cubed

Volume[rectangle]= (length)(width)

Answer 1

assuming the dimention of the cube is D, it is also the diameter of the sphere so the sphere's radius is D/2

volume of sphere is 4/3 pi r^3 = pi/6 D^3

volume of cube is D^3

so the ratio is pi/6, a little over 50%

Answer 2

21 minutes to 2hours