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Question
How many smaller cubes have at least two of their faces painted white?
How many smaller cubes have at least two of their faces painted white?
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Solution
The correct option is D 7
The cubes on the corner of each face will have three faces painted. There are 8 cubes in total.
Out of these 8 cubes, 4 cubes will have 2 faces painted black and 1 face painted white. The other four cubes will have 2 faces painted white and one face painted black.
The cubes lying in the middle of the cubes lying on the edge will have two of their faces painted. There will be 12 such cubes. 3 of these cubes will have two faces painted white. 3 of them will have 2 faces painted black. The rest will have one face painted white and the other black.
Thus, the total number of cubes with at least two faces painted white will be 7.
The cubes on the corner of each face will have three faces painted. There are 8 cubes in total.
Out of these 8 cubes, 4 cubes will have 2 faces painted black and 1 face painted white. The other four cubes will have 2 faces painted white and one face painted black.
The cubes lying in the middle of the cubes lying on the edge will have two of their faces painted. There will be 12 such cubes. 3 of these cubes will have two faces painted white. 3 of them will have 2 faces painted black. The rest will have one face painted white and the other black.
Thus, the total number of cubes with at least two faces painted white will be 7.
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