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?
+128474 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%
