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Directions to Solve
The following questions are based on the information given below:
All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.
Question -
How many small cubes are there whose only one face is coloured ?
  • a)
    32
  • b)
    8
  • c)
    16
  • d)
    24
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Directions to Solve ...
Number of small cubes having only one face coloured = 4 from each face
= 4 x 6
= 24
This question is part of UPSC exam. View all LR courses
Most Upvoted Answer
Directions to Solve ...
Understanding the Problem:
To solve this problem, we need to understand the given information. A big cube is colored on all opposite faces with red, black, and green colors. This big cube is then cut into 64 small equal cubes.

Identifying the Requirement:
We need to determine the number of small cubes that have only one face colored.

Solution Approach:
To find the number of small cubes with only one face colored, we can visualize the cube and understand the arrangement of the colors on the faces.
- Each small cube will have 6 faces.
- The cubes at the center of each face of the big cube will have 1 face colored.
- There will be 4 such cubes for each color (red, black, green) on each face of the big cube.
- Since there are 6 faces on the big cube, the total number of small cubes with only one face colored will be 4 (cubes per color) * 3 (colors) * 6 (faces) = 72.

Conclusion:
Therefore, there are 24 small cubes whose only one face is colored. So, the correct answer is option 'D'.
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