Question

A basketball is shipped in a cube-shaped box. The basketball just want touches the sides of the box. About what percent of the space in the cube is occupied by the basketball?

Answer 1

Volume
cube and sphere

the diameter of the sphere=height of box=legnth of box=width of box

volume of cube=side^3
volume of sphere=(4/3)pir^3

side=d=2r
Vcube=d^3

vsphere=(4/3)pi(d/2)^3
Vsphere=(pid^3)/6

percent
basketballV/boxV=( (pid^3)/6)/(d^3)=(pid^3)/(6d^3)=pi/3=aprox 0.523599=52.3599% (round if nececary)