A cube is painted blue on all faces and then cut into 125 cubes of equal size. How many cubes are painted on one face only?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 54
125 small cubes means each edge of the big cube is cut into \(n=5\) parts, since \(5^3=125\). A small cube has only one painted face when it lies on a face of the big cube but not on any edge: these are the inner squares of each face.
On each face, the inner square is \((n-2)\times(n-2)=3\times3=9\) cubes
The big cube has 6 faces, so \(6\times9=54\) cubes
Tip: For a painted cube cut into \(n^3\) small cubes: three faces painted \(=8\) (corners), two faces \(=12(n-2)\), one face \(=6(n-2)^2\), no face \(=(n-2)^3\).