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A 6” cube is painted on the outside and cut into 27 smaller cubes. What is the total of the areas of the unpainted surfaces?

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sqdancefan

Answer:

  432 square inches

Step-by-step explanation:

The 27 smaller cubes each have a dimension that is 1/∛27 = 1/3 the dimension of the larger cube. That is, each is a 2" cube. Their total surface area is ...

  (27 cubes)(6 faces/cube)((2 in)²/face) = 648 in²

The painted surface area of the larger cube is ...

  (6 faces/cube)((6 in)²/face) = 216 in²

Subtracting the painted cube area from the total cube area of the smaller cubes, we have an unpainted area of ...

  648 in² -216 in² = 432 in² . . . unpainted area

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