At an art exhibition, Amir displayed a solid model made from 24 identical cubes, each of side length 1 cm. The model measured 4 cm by 3 cm by 2 cm, and Amir painted all its outer surfaces red, including the bottom. How many small cubes had exactly 1 face painted red?
- 2
- 4
- 6
- 8
Need a hint?
Look for cubes that touch just one outside face and are away from all edges.
Worked answer
- A cube has exactly 1 painted face only if it is in the middle of a face, away from every edge.
- The model is only 2 cubes high, so on the 4 cm by 2 cm and 3 cm by 2 cm side faces every cube lies on an edge. None of them count.
- On the top face (4 by 3), the middle cubes form a (4 − 2) by (3 − 2) = 2 by 1 block: 2 cubes.
- The bottom face also has 2 such cubes.
- Cubes with exactly 1 face painted = 2 + 2 = 4.
Answer: 4 cubes
The mistake this question tests
Habit
Area and perimeter formulas
Some pupils count cubes on the edges or count only one of the two large faces. Such cubes have either 2 or 3 faces painted, or they miss half of the cubes with exactly 1 face painted.
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