A cube painted green on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
Cutting the cube into 27 equal cubes makes 3 layers of 3 × 3. A small cube has paint on one face only if it lies in the middle of a face, away from every edge and corner.
Each face of the big cube is a 3 × 3 square of small cubes; only its centre cube touches no edge, so 1 cube per face is painted on one face only
The cube has 6 faces, so \(6\times1=6\) small cubes
The others are 8 corner cubes (three painted faces), 12 edge cubes (two painted faces) and 1 cube in the very middle with no paint: \(8+12+6+1=27\).