Question:
A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?
A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?
Show Hint
Count how many small cubes lie along one edge, then remove the outer layer on each side.
Updated On: Nov 5, 2026
- 8
- 16
- 12
- 24
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Cubes along one edge:
12 / 3 = 4 small cubes along each edge, so there are 4 × 4 × 4 = 64 small cubes in all.
Step 2: Remove the outer layer:
Cubes with no painted face lie strictly inside, so we remove one layer from each side: 4 - 2 = 2 cubes along each edge of the inner block.
Step 3: Count the inner cubes:
2 × 2 × 2 = 8.
Final Answer:
The correct option is (1): 8
12 / 3 = 4 small cubes along each edge, so there are 4 × 4 × 4 = 64 small cubes in all.
Step 2: Remove the outer layer:
Cubes with no painted face lie strictly inside, so we remove one layer from each side: 4 - 2 = 2 cubes along each edge of the inner block.
Step 3: Count the inner cubes:
2 × 2 × 2 = 8.
Final Answer:
The correct option is (1): 8
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