If determining the volume of a rectangular box, five cubes were found to fit exactly along one edge, and four cubes were found to fit exactly along another edge. However, after six horizontal layers had been stacked in the box, a space at the top was left unfilled. a. If the height of the space was half the length of an edge of a cube, what was the volume of the box? b. If the height of the space was 0.23 of the length of an edge of a cube, what was the volume of the box?

To determine the volume of a rectangular box.

Let the edge of a cube be = a

Length of one edge of a rectangular box = five cubes = 5a

Length of another edge of a rectangular box = four cubes = 4a

a) Height of the rectangular box = six cubes + half the length of an edge of a cube

= 6a + 0.5a = 6.5a

Volume of a rectangular box = l x b x h = 5a x 4a x 6.5a = 130 a³

b) Height of the rectangular box = six cubes + 0.23 of the length of an edge of a cube

= 6a + 0.23a = 6.23a

Volume of a rectangular box = l x b x h = 5a x 4a x 6.23a = 124.6 a³