Question

All the surfaces of a cube of 15 cm side are painted with red colour and then it is cut into smaller cubes of 3 cm side. Then, how many smaller cubes are there having only one surface painted with red colour?

• A. 18
• B. 24
• C. 36
• D. 54

Hint:

For cube-cutting problems, classify cubes as corner, edge, and face cubes to determine their exposure to paint.

Answer 1

The Correct Option is C

1. The given cube has a side length of \(15\) cm.
2. It is divided into smaller cubes of \(3\) cm side.
- Number of small cubes along one edge = \( \frac{15}{3} = 5 \).
- Total number of smaller cubes = \( 5^3 = 125 \).
3. Small cubes with only one painted face are the cubes on the faces but not on edges or corners.
- Each face has a \(3 \times 3\) inner region where cubes have one face painted.
- Number of such cubes per face = \(3 \times 3 = 9\).
- Total for all 6 faces = \(9 \times 4 = 36\).
Thus, the number of cubes with only one painted face is 36.