8.8: Painted Cubes
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You can build up squares from smaller squares:
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1 × 1 square | 2 × 2 square | 3 × 3 square |
In a similar way, you can build up cubes from smaller cubes:
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1 × 1 × 1 cube[1] | 2 × 2 × 2 cube[2] | 3 × 3 × 3 cube[3] |
We call a 1 × 1 × 1 cube a unit cube.
Explain your answers.
Imagine you build a 3 × 3 × 3 cube from 27 small white unit cubes. Then you take your cube and dip it into a bucket of bright blue paint. After the cube dries, you take it apart, separating the small unit cubes.
Generalize your work on Problem 10. What if you started with a 2 × 2 × 2 cube? Answer the same questions. What about a 4 × 4 × 4 cube? How about an n × n × n cube? Be sure to justify what you say.