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Question

How many smaller cubes have three of their faces painted red?
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A
64
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B
4
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C
12
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D
8
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E
None of these
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Solution

The correct option is D 8
Here n = 3.
Therefore, number of cubes with 3 sides painted red = Number of corner cubes = 8.
Number of cubes with 2 faces painted = (n2)×12=(32)×12=12.
Number of cubes with 1 face painted = (n2)2×6=(32)2×6=6.
Number of cubes with no face painted = (n2)3=(32)3=1

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