### Exercise :: Cube and Cuboid - Cube and Cuboid 5

- Cube and Cuboid - Introduction
- Cube and Cuboid - Cube and Cuboid 1
- Cube and Cuboid - Cube and Cuboid 2
- Cube and Cuboid - Cube and Cuboid 3
- Cube and Cuboid - Cube and Cuboid 4
- Cube and Cuboid - Cube and Cuboid 5
- Cube and Cuboid - Cube and Cuboid 6
- Cube and Cuboid - Cube and Cuboid 7
- Cube and Cuboid - Cube and Cuboid 8
- Cube and Cuboid - Cube and Cuboid 9

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.

1. | How many small cubes are there where one face is green and other one is either black or red ? |
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Answer: Option C Explanation: Number of small cubes having one face green and the other one is either red or black = 8 x 2 = 16 |

2. | How many small cubes are there whose no faces are coloured ? |
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Answer: Option C Explanation: Number of small cubes having no face coloured = (x - 2) = (4 - 2) = 8 |

3. | How many small cubes are there whose 3 faces are coloured ? |
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Answer: Option B Explanation: Number of small cubes having three faces coloured = 1 at each corner = 1 x 8 = 8 > |

4. | How many small cubes are there whose only one face is coloured ? |
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Answer: Option D Explanation: Number of small cubes having only one face coloured = 4 from each face = 4 x 6 = 24 |

5. | How many small cubes are there whose at the most two faces are coloured ? |
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Answer: Option B Explanation: Number of small cubes having two faces coloured = 8 + 8 + 4 + 4 = 24 and Number of small cubes having only one face coloured = 4 x 6 = 24 and Number of small cubes having no face coloured = 4 + 4 = 8 Therefore, total number of small cubes whose at the most two faces are coloured = 24 + 24 + 8 = 56. |