Question

A cube is painted Blue on all faces and is then cut into 125 cubes of equal size. How many cubes are not painted on any face?

• A. 8
• B. 16
• C. 27
• D. 36

Hint:

Use formula \((n - 2)^3\) for unpainted cubes inside a painted cube of side \(n\).

Answer 1

The Correct Option is C

Total small cubes = \(125 = 5^3\). This means the original cube was divided into a \(5 \times 5 \times 5\) cube. To find the cubes not painted on any face, we count the completely internal cubes: Only the inner \(3 \times 3 \times 3\) cube will remain unpainted. \[ (5 - 2)^3 = 3^3 = \boxed{27} \]