Question 657047
We want to calculate the volume of the three balls, and the volume of the box.
The amount of empty space will be the difference: the volume of the box minus the volume of the balls.
 
The volume of a box shaped prism is calculated by multiplying all three dimensions: width of the base, length of the base and height.
The width and length of the square base of the box will be the diameter of a ball: {{{1.68}}} inches.
The height of the box will be three times that,
{{{3*1.68}}} inches = {{{5.04}}}  inches.
The volume of the box is
{{{1.68*1.68*5.04}}}  cubic inches = {{{14.22}}} cubic inches (rounded to two decimal places).
 
The volume, {{{V}}} of a sphere of radius {{{r}}} can be calculated using the formula
{{{V=(4/3)*pi*r^3}}}
The radius is half of the diameter, so the radius of a ball would be
{{{1.68inches/2=0.84inch}}}
You will have to round the value of {{{pi}}} in your calculations,
As you multiply to get {{{r^3}}} and the volume, you will end with way too many digits, so you will want to round again.
Using {{{pi=3.14}}} (rounded), the volume of one ball is
{{{V=(4/3)*3.14*0.84^3=(4/3)*3.14*0.593=2.48}}} cubic inches (rounding at each step of the calculation)
The volume of all 3 balls would be {{{3*2.48}}} cubic inches = {{{7.44}}} cubic inches.
 
The difference is the amount of empty space in the box:
{{{14.22}}} cubic inches - {{{7.44}}} cubic inches = {{{6.78}}} cubic inches.