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?

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)