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All the opposite faces of a big cube are coloured with red, black and green colours. After that, is cut it into 64 small equal cubes. In each of the following questions, select the correct option for the questions asked.
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?
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Most Upvoted Answer
All the opposite faces of a big cube are coloured with red, black and ...
To solve this problem, we need to visualize the cube and understand the different possibilities for the colors of the small cubes.
First, let's consider the opposite faces of the big cube. There are three pairs of opposite faces: one pair is red, one pair is black, and one pair is green.
Now, let's think about how the cube is cut into smaller cubes. Since the cube is divided into 64 small equal cubes, we can imagine that it is divided into 4 layers of 4x4 cubes each.
Now, let's analyze the possible colors of the small cubes. For a small cube to have one face green and the other face either black or red, it means that we need to consider the cubes on the edges of the big cube.
There are 4 cubes on each edge of the big cube. Since there are 12 edges in total, there are a total of 48 small cubes on the edges.
Out of these 48 cubes, only half of them will have one face green and the other face either black or red. This is because each edge has two cubes with one face green and the other face either black or red.
Therefore, the number of small cubes where one face is green and the other one is either black or red is 48/2 = 24.
Hence, the correct answer is option 'C' - 16.
First, let's consider the opposite faces of the big cube. There are three pairs of opposite faces: one pair is red, one pair is black, and one pair is green.
Now, let's think about how the cube is cut into smaller cubes. Since the cube is divided into 64 small equal cubes, we can imagine that it is divided into 4 layers of 4x4 cubes each.
Now, let's analyze the possible colors of the small cubes. For a small cube to have one face green and the other face either black or red, it means that we need to consider the cubes on the edges of the big cube.
There are 4 cubes on each edge of the big cube. Since there are 12 edges in total, there are a total of 48 small cubes on the edges.
Out of these 48 cubes, only half of them will have one face green and the other face either black or red. This is because each edge has two cubes with one face green and the other face either black or red.
Therefore, the number of small cubes where one face is green and the other one is either black or red is 48/2 = 24.
Hence, the correct answer is option 'C' - 16.
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Community Answer
All the opposite faces of a big cube are coloured with red, black and ...
Number of small cubes having one face green and the other one is either red or black = 8 × 2 = 16
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All the opposite faces of a big cube are coloured with red, black and green colours. After that, is cut it into 64 small equal cubes. In each of the following questions, select the correct option for the questions asked.How many small cubes are there where one face is green and other one is either black or red?a)28b)8c)16d)24Correct answer is option 'C'. Can you explain this answer?
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