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Question

A cube of 4 cm has been painted on its surfaces in such a way that two opposite surfaces have been painted blue and two adjacent surfaces have been painted red. Two remaining surfaces have been left unpainted. Now the cube is cut into smaller cubes of side 1 cm each.

How many cubes will have at least red colour on its surfaces?


A
2
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B
22
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C
28
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D
32
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Solution

The correct option is B 28
Two adjacent surfaces have been painted red and if cut these surface into 1 cm length then we would get many small cube of side 1 cm, and so one surface of big cube will form $$ 4 *4 = 16$$ surfaces of small cube. 
Now as per given statement in question, "
two adjacent surfaces have been painted red" That means adjacent surface will also form $$ 4*4 = 16 $$ small cube with red paint. 
So total cube of red colour might be $$ 16+16 =32$$ . 
But the four cubes are common in both the red colour surfaces.
Thus, total cubes having at least red colour on its surfaces will be $$32-4=28$$.
Hence, Option "C" is correct answer.     

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Logical Reasoning

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