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Question

# A cube whose two adjacent faces are coloured is cut into 64 identical small cubes. How many of those small cubes are not coloured at all?

A
24
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B
32
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C
36
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D
48
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Solution

## The correct option is A 24The cube is coloured on two adjacent faces(let's take that sides as top and back surfaces).So, the cubes on the surface having no colour will be12 cubes on the front surface.6,6 cubes on right and left surface and 4 cubes at the bottom surface.So, total cubes on the surface with no colour are 12+6+6+4=28.The small cubes which are enclosed in the big cube are only 8 and they won't have a colour.Thus, the total no. of cubes with no colour=28+8=36.Hence, option C is correct.

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