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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 with 3 faces coloured?
- a)4
- b)8
- c)16
- d)24
Correct answer is option 'B'. Can you explain this answer?
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All the opposite faces of a big cube are coloured with red, black and ...
Solution:
Total number of small cubes = 64
Each face of the big cube is coloured with three colours, i.e., red, black and green. Therefore, each face has three small squares of different colours.
Number of small cubes with three faces coloured = Number of small cubes with one face of each colour.
We can find the number of small cubes with one face of each colour as follows:
- There are 4 corners of the big cube. Each corner has 3 small cubes with one face of each colour. Therefore, total number of small cubes with one face of each colour at the corners = 4 × 3 = 12.
- There are 24 edges of the big cube. Each edge has 2 small cubes with one face of each colour. Therefore, total number of small cubes with one face of each colour at the edges = 24 × 2 = 48.
- There are 36 small squares on the faces of the big cube. Each small square has 1 small cube with one face of each colour. Therefore, total number of small cubes with one face of each colour on the faces = 36 × 1 = 36.
Total number of small cubes with one face of each colour = 12 + 48 + 36 = 96
Each small cube with one face of each colour has 3 faces coloured. Therefore, the number of small cubes with 3 faces coloured = 96/3 = 32.
Hence, the correct option is B) 8.
Total number of small cubes = 64
Each face of the big cube is coloured with three colours, i.e., red, black and green. Therefore, each face has three small squares of different colours.
Number of small cubes with three faces coloured = Number of small cubes with one face of each colour.
We can find the number of small cubes with one face of each colour as follows:
- There are 4 corners of the big cube. Each corner has 3 small cubes with one face of each colour. Therefore, total number of small cubes with one face of each colour at the corners = 4 × 3 = 12.
- There are 24 edges of the big cube. Each edge has 2 small cubes with one face of each colour. Therefore, total number of small cubes with one face of each colour at the edges = 24 × 2 = 48.
- There are 36 small squares on the faces of the big cube. Each small square has 1 small cube with one face of each colour. Therefore, total number of small cubes with one face of each colour on the faces = 36 × 1 = 36.
Total number of small cubes with one face of each colour = 12 + 48 + 36 = 96
Each small cube with one face of each colour has 3 faces coloured. Therefore, the number of small cubes with 3 faces coloured = 96/3 = 32.
Hence, the correct option is B) 8.
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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 three faces coloured = 1 at each corner = 1 × 8 = 8
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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 with 3 faces coloured?a)4b)8c)16d)24Correct answer is option 'B'. Can you explain this answer?
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