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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 where one face is green and other one is either black or red ?
  • a)
    28
  • b)
    8
  • c)
    16
  • d)
    24
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Directions to Solve ...
Number of small cubes having one face green and the other one is either red or black = 8 x 2 = 16
This question is part of UPSC exam. View all LR courses
Most Upvoted Answer
Directions to Solve ...
Solution:

Given information:
- A big cube with opposite faces coloured with red, black and green colours is cut into 64 small equal cubes.

To find:
Number of small cubes where one face is green and the other one is either black or red.

Approach:
- We can start by visualizing the big cube and the small cubes after it is cut.
- Then we can count the number of small cubes which have one face green and the other face either black or red.

Visualizing the cube:
- A big cube has 6 faces.
- Opposite faces of the cube are coloured with red, black and green colours.
- So, there are 2 red faces, 2 black faces and 2 green faces.
- The cube is cut into 64 small equal cubes.
- Each small cube has 6 faces.

Counting the small cubes:
- Let's count the number of small cubes which have one face green and the other face either black or red.
- There are 4 corner small cubes which have one face green and the other two faces either black or red.
- There are 4 small cubes in the middle of each face which have one face green and the other three faces either black or red.
- So, there are 4 corner small cubes and 4 small cubes in the middle of each face which have one face green and the other face either black or red.
- Total number of such small cubes = 4 + (4 x 6) = 28.

Answer:
- The number of small cubes where one face is green and the other one is either black or red is 28.
- Therefore, the correct option is (a) 28.
Community Answer
Directions to Solve ...
24
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