Question

Direction: A cube is painted blue on all faces and is then cut into 125 cubes of equal size.

How many cubes are not painted on any face?

1. 8
2. 16
3. 27
4. 36

Answer 1

Correct Answer - Option 3 : 27

The cube is cut into 125 small cubes. Here, n = 5

1) Number of cubes will have three faces painted = 8 (because 8 corners)

2) Number of cubes will have two faces painted = (n - 2) × number of edges = (5 - 2) × 12 = 36

3) Number of cubes will have one faces painted = (n - 2)² × 6 = (5 - 2)² × 6 = 54 

4) Number of cubes will have no faces painted = (n - 2)³ = (5 - 2)³ = 27

Hence, "27" is the correct answer.