Cubes

A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces?

  1. 12
  2. 8
  3. 6
  4. 4

Answer

On cutting the cube (3×3×3), 27 cubes (1×1×1) will be formed. You can exclude eight cubes at the corners, as three faces are painted. You can also exclude one central cube, as it's face is not painted. The middle cubes of each face can be excluded, as only one face is painted. That counts to six cubes. The rest of the cubes (1×1×1) will be painted on two faces.

So, 27 - (8+1+6) = 12

If you cut the cube into 1 cm cubes, each side will have nine squares. Every corner will have 3 painted faces and every middle piece 1 painted face. That means each edge will have one piece with two painted faces. On a cube there are 12 edges, thus there will be 12 small cubes with 2 painted faces on it.

The correct option is A.