UPSC Prelims 2018 · CSAT
Question 35: Basic Numeracy
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?
AnswerUPSC’s answer is (a).
A 3 cm cube cut into 1 cm cubes gives 27 small cubes: 8 corners (three painted faces), 12 edge cubes that are not corners (two painted faces), 6 face-centre cubes (one painted face) and 1 hidden centre cube (none). Each edge of length 3 has 3 - 2 = 1 middle cube, and a cube has 12 edges, so 12 small cubes have exactly two painted faces. Check: 8 + 12 + 6 + 1 = 27.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Correct: 12 edges × 1 middle cube each.
- (b) 8 is the number of corner cubes, with three painted faces.
- (c) 6 is the number of face-centre cubes, with one painted face.
- (d) 4 matches no category of cubes in a 3 × 3 × 3 cube.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2018, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.