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Question
Two hundred and sixteen cubes of the same size are arranged in the form of a cube on a table. A column of six cubes is removed from each of the four corners. Then, all the exposed faces of the solid (except the face touching the table) are coloured black. Now, answer these questions based on the above information:
How many cubes do not have any face colored black?
Two hundred and sixteen cubes of the same size are arranged in the form of a cube on a table. A column of six cubes is removed from each of the four corners. Then, all the exposed faces of the solid (except the face touching the table) are coloured black. Now, answer these questions based on the above information:
How many cubes do not have any face colored black?
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Solution
The correct option is B 80
Number of cubes = 6*6*6 – (4*6) = 192
Now, imagine cutting out all the vertical edges. The remaining shape will have twice the number of edges and corners.
43 = 64 cubes are inner (core) cubes with no faces exposed.
Now, apart from the 64 inner cubes, the middle cubes at the bottom face will also have no colour 16 cubes.
Total = 80 cubes.
Number of cubes = 6*6*6 – (4*6) = 192
Now, imagine cutting out all the vertical edges. The remaining shape will have twice the number of edges and corners.
43 = 64 cubes are inner (core) cubes with no faces exposed.
Now, apart from the 64 inner cubes, the middle cubes at the bottom face will also have no colour 16 cubes.
Total = 80 cubes.
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