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Question
How many smaller cubes have three of their faces coloured?
How many smaller cubes have three of their faces coloured?
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Solution
The correct option is B 1
The cube is painted on three adjacent faces and cut into 64 smaller, identical cubes. In this case, only one corner cube is painted on three of its faces.
Each pair, out of three coloured adjacent faces, has only one common edge. Thus, there are three edges, along which two coloured faces meet. There are three smaller cubes along each such edge which are painted only on two of their faces. Hence, there are totally 3×3=9 smaller cubes which are coloured on two of their faces.
There are 9 smaller cubes on each coloured face which are coloured only on one of their faces. Thus, there are totally 9×3=27 smaller cubes which are coloured only on one of their faces.
The cube is painted on three adjacent faces and cut into 64 smaller, identical cubes. In this case, only one corner cube is painted on three of its faces.
Each pair, out of three coloured adjacent faces, has only one common edge. Thus, there are three edges, along which two coloured faces meet. There are three smaller cubes along each such edge which are painted only on two of their faces. Hence, there are totally 3×3=9 smaller cubes which are coloured on two of their faces.
There are 9 smaller cubes on each coloured face which are coloured only on one of their faces. Thus, there are totally 9×3=27 smaller cubes which are coloured only on one of their faces.
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