Nurul dipped a rectangular bar of soap measuring 9 cm by 5 cm by 4 cm completely into blue dye. After the dye dried, she cut the soap into 1-cm cubes. How many small cubes had exactly two faces dyed blue?
- 56
- 48
- 40
- 28
Need a hint?
Consider the four edges of each length, but exclude the corner cubes.
Worked answer
- A cube with exactly two dyed faces lies along an edge of the bar but is not a corner cube.
- Along each edge, leave out the 2 corner cubes: the 9-cm edges have 9 − 2 = 7, the 5-cm edges have 5 − 2 = 3 and the 4-cm edges have 4 − 2 = 2.
- There are 4 edges of each length: 4 × (7 + 3 + 2) = 4 × 12 = 48.
- So 48 small cubes have exactly two faces dyed.
Answer: 48 cubes
The mistake this question tests
Habit
Calculation slip
A common mistake is to include the 8 corner cubes. Each corner cube has three dyed faces, not two.
How to fix it at home →Wrong answers children often give:
- 56 Calculation slip
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