A cube of 5cm is painted on all its faces. If it is sliced into 1 cubic centimeter cubes, how many one centimeter cubes will have exactly one of their faces painted?

Question

Philoid · Accepted Answer

The side of the cube = 5 cm is painted on all sides. Its figure is shown below:

We can say that the side of 5 cm is made up of 5 parts each of 1 cm.

Total number of cubes of side 1 cm = 25 + 25 + 25 + 25 + 25 = 125.

Now, the cubes whose one face is painted are marked in red colour.

As seen above, in one face of cube total 9 small cubes have 9 one side painted.

And, there are 6 faces in a cube.

Hence, total 9 × 6 = 54 faces will have one face painted.