Question

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

How many cubes are painted on one face only?

1. 16
2. 32
3. 48
4. 54

Answer 1

Correct Answer - Option 4 : 54

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, "54" is the correct answer.