A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces?
- (a) 12 ✓ UPSC's answer
- (b) 8
- (c) 6
- (d) 4
Why the answer is (a)
• The 3 cm cube is cut into 3 × 3 × 3 = 27 cubes of 1 cm.
• Cubes with exactly two painted faces lie on the edges of the big cube but not at its corners.
• Each of the 12 edges has 3 small cubes: 2 corner cubes and 1 middle cube.
• So 12 × 1 = 12 small cubes have exactly two painted faces, option (a).
Why the other options are wrong
- (b) 8
- 8 is the number of corner cubes, which have three painted faces, not two.
- (c) 6
- 6 is the number of faces on the cube, not the count of edge-center cubes.
- (d) 4
- 4 is the number of cubes on one face of the 3x3 grid excluding the center, which is irrelevant to the edge calculation.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.