Question

a sealed rectangular box measuring 8 x 6 x 18 contains 864 sugar cubes, each measuring 1 x 1 x 1. How many sugar cubes are touching the box ?

Answer 1

The surface area of each face of a sugar cube is 1*1 = 1 units²

The rectangular box has 6 faces in contact with sugar cubes.
The area of each of two faces is 18*6 = 108 units²
Therefore these two faces touch 2*108 = 216 cubes

There are two other faces each of area 18*8 = 144 units²
Therefore these two faces touch 288 cubes.

There are another two faces, each of area 6*8 = 48 units².
Therefore these faces touch 96 cubes.

The total number of cubes touching the faces of the box are
216 + 288 + 96 = 600

Answer: 600 cubes