A cube of side 12 cm, is painted red on all the faces and then cut into…
2023
A cube of side 12 cm, is painted red on all the faces and then cut into smaller cubes, each of side 3cm. What is the total number of smaller cubes having none of their faces painted?
- A.
8
- B.
16
- C.
32
- D.
64
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Step 1: Find how many small cubes fit along one edge.
Calculation: 12 ÷ 3 = 4 small cubes per edge.
Step 2: Total number of small cubes after cutting.
Total = 4^3 = 64 small cubes.
Step 3: Count the small cubes that have no painted faces.
Only the interior small cubes (not on any face) are unpainted. These form a smaller cube obtained by removing the outer layer on each side, so its edge length is (4 − 2) = 2.
Number of unpainted cubes = 2^3 = 8.
Answer: 8