A solid wooden cube of edge length $6\text{ cm}$ is painted blue on all six faces and then sliced into identical smaller cubes of edge length $1\text{ cm}$. The number of small cubes that have EXACTLY ONE face painted blue is ________ (answer in integer).
Answer Key:
96
Step-by-Step Solution & Explanation
For a cube divided into $n^3$ small cubes where $n = \frac{6\text{ cm}}{1\text{ cm}} = 6$:
- Cubes with exactly 1 face painted lie in the interior of each of the 6 square faces.
- Number of interior cubes per face $= (n - 2)^2 = (6 - 2)^2 = 4^2 = 16$.
- Total for all 6 faces $= 6 \times (n - 2)^2 = 6 \times 16 = 96$.
Thus, exactly 96 small cubes have only one painted face.