A gumball machine is in the shape of a sphere with a radius of 6 inches. A store manager wants to fill up the machine with miniature gumballs, which have a radius of 1/3in. How many gumballs will fit in the machine?

To know how many gumballs will fit in the machine, the volume of the minature and the machine should be calculated. Volume of sphere:

V = (4/3) pi * r^3

Volume of the machine r = 6 in

V = (4/3) pi * 6^3 = 904.77 in3

Volume of the miniature gumballs

V = (4/3) pi * (1/3) ^3 = 0.1551 in3

Divide the two volume to get the number of gumballs that can fill the machine

904.77 in3 / 0.1551 in3 = 5832