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64 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have no face painted at all?a.16b.8c.12d.10

Question

64 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have no face painted at all?a.16b.8c.12d.10

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Solution

The larger cube is formed by stacking the smaller cubes in a 4x4x4 arrangement (since 4^3 = 64).

When the larger cube is painted, only the outer layer of smaller cubes gets painted. This means that the smaller cubes in the interior, which form a 2x2x2 cube, remain unpainted.

So, the number of smaller cubes that have no face painted at all is 2^3 = 8.

Therefore, the answer is b.8.

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