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Question
How many cubes are uncoloured on all the faces?
How many cubes are uncoloured on all the faces?
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Solution
The correct option is C 48
As per the problem, the cube is divided into 125 equal small cubes. That means, the cube is being cut into 5 slices horizontally and vertically resulting in 5x(5x5) smaller cubes.
The uncoloured faces would be adjacent since red & green faces are opposite and yellow & blue faces are adjacent. Suppose, their labels are UC1 and UC2. On UC1, 12 cubes would be without any coloured face. On UC2, 4 horizontal levels would have similar pattern. Therefore, total numbers of cubes without any coloured face would be 12 x 4 = 48.
Hence, correct answer is (C)
As per the problem, the cube is divided into 125 equal small cubes. That means, the cube is being cut into 5 slices horizontally and vertically resulting in 5x(5x5) smaller cubes.
The uncoloured faces would be adjacent since red & green faces are opposite and yellow & blue faces are adjacent. Suppose, their labels are UC1 and UC2. On UC1, 12 cubes would be without any coloured face. On UC2, 4 horizontal levels would have similar pattern. Therefore, total numbers of cubes without any coloured face would be 12 x 4 = 48.
Hence, correct answer is (C)
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