Discussion
How many smaller cubes are there having only one surface painted with red color ?
Answer: D
There are 54 cubes with only one face painted.
A 15 cm cube cut into 3 cm cubes has \(15 / 3 = 5\) small cubes along each edge. Cubes with exactly one painted face lie in the middle of each face, away from the edges: a \(3 \times 3\) block on each face.
\[ 6 \times (5 - 2)^{2} = 6 \times 9 = 54 \]
The full breakdown of the 125 small cubes is: 8 corner cubes with three painted faces, \(12 \times 3 = 36\) edge cubes with two, 54 face cubes with one, and \(3^{3} = 27\) inner cubes with none; no cube has four or more painted faces. Check: \(8 + 36 + 54 + 27 = 125\).
36 is the count of edge cubes (two painted faces), not one-face cubes, and 24 and 17 do not match any category.
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