125 small but identical cubes are put together to form a large cube. This…
2025
125 small but identical cubes are put together to form a large cube. This large cube is now painted on all six faces. How many of the smaller cubes have no face painted at all ?
- A.
27
- B.
64
- C.
36
- D.
8
Attempted by 294 students.
Show answer & explanation
Correct answer: A
Answer: 27
Step 1: Find the side length of the large cube.
Since 125 = 5^3, the large cube is 5 × 5 × 5 small cubes.
Step 2: Determine which small cubes remain unpainted.
Only the interior small cubes have no painted face. Removing the outer layer on each face reduces the side length by 2, so the interior side length is 5 − 2 = 3.
Step 3: Compute the number of interior (unpainted) cubes.
Number unpainted = 3^3 = 27.
Large cube side = 5
Interior side = 5 − 2 = 3
Unpainted small cubes = 3^3 = 27