Problem 5 · Sort by position, then count · 4 points
Made by AI and not reviewed by a real person.
A large cube is painted red on the outside and then cut into 27 equal small cubes (3 × 3 × 3). How many small cubes have exactly ONE red face?
- 6
- 8
- 26
- 12
- 1
Show a hint
- Where can a cube with exactly one painted face sit: corner, edge, middle of a face, or center?
Show the answer and solution
Answer: A — 6
Classify by position: corners (8) have 3 painted faces, edge cubes (12) have 2, the hidden center (1) has 0, and the middle cube of each face has exactly 1 — one per face, 6 faces → 6 cubes. Classifying objects by role before counting turns a 3-D headache into simple bookkeeping.