A cube is colored red on all the faces. It is cut into 125 smaller cubes of equal size. How many cubes are colored on one face only?

Correct option is C

Given that a cube is colored red on all faces and then cut into 125 smaller cubes of equal size, we need to determine how many of these smaller cubes are colored on only one face.
Step 1: Analyze the problem:
- The original cube is cut into 125 smaller cubes, which implies that the original cube was a (5 × 5 × 5) cube because (53 = 125).
Step 2: Identify the cubes with one face colored:
- The cubes that have only one face colored are those that are on the faces of the large cube but not on the edges.
- For a (5 × 5) face of the large cube, the cubes along the edges of the face have two or three faces colored, so we focus on the inner (3 × 3) area of each face.
Step 3: Calculate the number of cubes with one face colored:
- Each face of the large cube has (3 × 3 = 9) cubes that have only one face colored.
- Since the large cube has 6 faces, the total number of cubes with one face colored is:
6 × 9 = 54