Question

A solid wooden cube is painted blue on all its faces, the cube is then cut into smaller cubes with each edge one-sixth of the edge of the original cube. How many of the smaller cubes will have only one face obtained?

Answer 1

Step 1: Finding the total number of small cubes formed

The cube is cut into smaller cubes, With each edge one-sixth of the edge of the original cube.

Therefore, the total number of smaller cubes formed$=6\times 6\times 6=216$ cubes.

Step 2: Finding the number of cubes with only one face painted.

Now cube adjacent to the edges will have more than one face painted. [For reference look at the figure]

Hence, the number of cubes having only one face painted$=6\times 4\times 4=96$cubes.

Therefore, $96$ smaller cubes will have only one face painted.