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Home › Non-Verbal Reasoning › Non-Verbal Reasoning - Cube Painting and Cutting

Non-Verbal Reasoning - Cube Painting and Cutting — Non-Verbal Reasoning Questions & Practice

Practise 215 Non-Verbal Reasoning - Cube Painting and Cutting questions from Non-Verbal Reasoning for competitive exams such as UPSC, Banking, SSC and Railway. Read the worked questions below, check every answer with an explanation, and track what you get wrong.

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Practice questions on Non-Verbal Reasoning - Cube Painting and Cutting — with answers

Try each question first, then open the answer. Explanations are included.

1. A cube of side 8 units is painted on all six faces and then cut into 8x8x8 smaller unit cubes. How many of the smaller cubes have exactly 1 face painted?

  1. A296
  2. B72
  3. C216
  4. D8
Show answer

Answer: C

Cubes with exactly 1 face painted lie at the centre of each face (excluding edges): 6 x (side - 2)^2 = 6 x 6^2 = 216.

2. A cube of side 38 units is painted on all six faces and then cut into 38x38x38 smaller unit cubes. How many of the smaller cubes have exactly 3 faces painted?

  1. A8
  2. B432
  3. C7776
  4. D54872
Show answer

Answer: A

Exactly 3 faces are painted only on the 8 corner cubes of any cube, regardless of its size (as long as the side is at least 2 units).

3. A cube of side 19 units is painted on all six faces and then cut into 19x19x19 smaller unit cubes. How many of the smaller cubes have exactly 3 faces painted?

  1. A4913
  2. B204
  3. C8
  4. D1946
Show answer

Answer: C

Exactly 3 faces are painted only on the 8 corner cubes of any cube, regardless of its size (as long as the side is at least 2 units).

4. A cube of side 38 units is painted on all six faces and then cut into 38x38x38 smaller unit cubes. How many of the smaller cubes have at least 1 face painted?

  1. A432
  2. B8216
  3. C8
  4. D54872
Show answer

Answer: B

Total cubes (54872) minus completely unpainted internal cubes (46656) = 8216.

5. A cube of side 5 units is painted on all six faces and then cut into 5x5x5 smaller unit cubes. How many of the smaller cubes have at least 1 face painted?

  1. A98
  2. B8
  3. C27
  4. D125
Show answer

Answer: A

Total cubes (125) minus completely unpainted internal cubes (27) = 98.

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