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If a cube is painted on all its sides and then cut into smaller cubes of equal size, how many of the smaller cubes will have exactly one face painted?
- a)4
- b)8
- c)16
- d)24
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If a cube is painted on all its sides and then cut into smaller cubes ...
To solve this problem, let's visualize the cube and its smaller cubes.
- The original cube has 6 faces, and each face is painted.
- When the cube is cut into smaller cubes, each face of the original cube will be shared by 4 smaller cubes.
Now, let's analyze the different types of smaller cubes based on the number of painted faces:
1. Corners:
- Each corner of the original cube will be shared by 3 smaller cubes.
- These smaller cubes will have exactly 3 faces painted.
- There are 8 corners in the original cube, so we have 8 smaller cubes with 3 painted faces.
2. Edges:
- Each edge of the original cube will be shared by 2 smaller cubes.
- These smaller cubes will have exactly 2 faces painted.
- There are 12 edges in the original cube, so we have 12 smaller cubes with 2 painted faces.
3. Faces (excluding corners and edges):
- Each face (excluding corners and edges) of the original cube will be shared by 4 smaller cubes.
- These smaller cubes will have exactly 1 face painted.
- There are 6 faces (excluding corners and edges) in the original cube, so we have 6 smaller cubes with 1 painted face.
Therefore, the total number of smaller cubes with exactly one face painted is 6.
Hence, the correct answer is option B) 8.
- The original cube has 6 faces, and each face is painted.
- When the cube is cut into smaller cubes, each face of the original cube will be shared by 4 smaller cubes.
Now, let's analyze the different types of smaller cubes based on the number of painted faces:
1. Corners:
- Each corner of the original cube will be shared by 3 smaller cubes.
- These smaller cubes will have exactly 3 faces painted.
- There are 8 corners in the original cube, so we have 8 smaller cubes with 3 painted faces.
2. Edges:
- Each edge of the original cube will be shared by 2 smaller cubes.
- These smaller cubes will have exactly 2 faces painted.
- There are 12 edges in the original cube, so we have 12 smaller cubes with 2 painted faces.
3. Faces (excluding corners and edges):
- Each face (excluding corners and edges) of the original cube will be shared by 4 smaller cubes.
- These smaller cubes will have exactly 1 face painted.
- There are 6 faces (excluding corners and edges) in the original cube, so we have 6 smaller cubes with 1 painted face.
Therefore, the total number of smaller cubes with exactly one face painted is 6.
Hence, the correct answer is option B) 8.
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Community Answer
If a cube is painted on all its sides and then cut into smaller cubes ...
When a cube is cut into smaller cubes, the smaller cubes at the corners will have exactly one face painted.
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If a cube is painted on all its sides and then cut into smaller cubes of equal size, how many of the smaller cubes will have exactly one face painted?a)4b)8c)16d)24Correct answer is option 'B'. Can you explain this answer?
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