A rectangular box has interior dimensions 6-inches by 5-inches by 10-inches. The box is filled with as many solid 2-inch cubes as possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes?
To make things easy, let the box length = 6 and the box width =10 and the box height = 5
We can put 3 cubes along the length and 5 cubes along the width.....thus....each layer of cubes contains 3 x 5 = 15 cubes
And we can stack 2 layers of cubes = 2x15 = 30 cubes in total
The volume of the box is 6 * 5 * 10 = 300 in^3
The volume of the cubes = 2^3 * 30 = 240 in^2
% of box volume taken up by the cubes = 240 / 300 = 8/10 = 80%