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?

We are given the dimensions of the box

8 x 6 x 18

So, the total volume of the box is

Vb = 8 x 6 x 18

Vb = 864 cubic units

We are also given the dimensions of sugar cubes

1 x 1 x 1

So, the volume of each cube is

Vc = 1 x 1 x 1

Vc = 1 cubic units

There are 864 sugar cubes inside the box. Assuming that the sugar cubes are stacked and arranged side by side leaving no spaces between them, the volume occupied by the sugar cubes is

V = 864 cubic units

So, all the cubes fit all the spaces inside the box

Next, the problem asks for the number of sugar cubes that touch the box.

We simply get the surface area of the box and subtract the common sugar cubes.

So,

8 x 6 + 8 x 18 + 6 x 18 - (2 x 8 + 2 x 6 + 2 x 18)

= 236 sugar cubes touch the box