There is a 4 inch cube painted on all sides. This is cut into number of 1 inch…
2023
There is a 4 inch cube painted on all sides. This is cut into number of 1 inch cubes. What is the number of cubes which have no painted sides.
- A.
8 cubes
- B.
4 cubes
- C.
6 cubes
- D.
None of these
Attempted by 11 students.
Show answer & explanation
Correct answer: A
Quick method: For an n×n×n cube cut into 1-inch cubes, the number of small cubes with no painted sides is (n−2)^3.
Step 1: Here n = 4, so the whole cube produces 4^3 = 64 small cubes.
Step 2: Remove the outer painted layer (one unit thick) from each side, leaving an inner block of (4−2) × (4−2) × (4−2) = 2 × 2 × 2.
Step 3: Number of unpainted cubes = 2^3 = 8.
Answer: 8 cubes have no painted sides.