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A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces?
- a)12
- b)8
- c)6
- d)4
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A solid cube of 3 cm side, painted on all its faces, is cut up into sm...
If you cut the cube into 1 cm cubes, each side will have nine squares. Every corner will have 3 painted faces and every middle piece 1 painted face. That means each edge will have one piece with two painted faces. On a cube there are 12 edges, thus there will be 12 small cubes with 2 painted faces on it.
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A solid cube of 3 cm side, painted on all its faces, is cut up into sm...
Given: A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side.
To find: How many of the small cubes will have exactly two painted faces?
Solution:
The given cube is of 3 cm side, so it can be divided into 27 smaller cubes of 1 cm side.
Let's consider the number of cubes with different number of painted faces:
1. Number of cubes with 0 painted faces:
As the given cube is painted on all its faces, there won't be any cube with 0 painted faces.
2. Number of cubes with 1 painted face:
Each face of the given cube is painted, so the cubes with 1 painted face will be the ones that have an edge on any of the faces of the given cube. So, there will be 12 such cubes.
3. Number of cubes with 2 painted faces:
The cubes with 2 painted faces will be the ones that have two of their faces on the adjacent edges of the given cube. So, there will be 6 such cubes.
4. Number of cubes with 3 painted faces:
Each corner of the given cube will have three of its faces painted, so there will be 8 such cubes.
5. Number of cubes with 4 painted faces:
In the given cube, the center cube will have all its faces painted, so there will be only one cube with 4 painted faces.
6. Number of cubes with 5 painted faces:
As there are no cubes with 0 painted faces, there won't be any cube with 5 painted faces.
7. Number of cubes with 6 painted faces:
As there are no cubes with 0 painted faces, there won't be any cube with 6 painted faces.
Therefore, the total number of cubes with exactly 2 painted faces will be 6. Hence, the correct option is (d) 12.
To find: How many of the small cubes will have exactly two painted faces?
Solution:
The given cube is of 3 cm side, so it can be divided into 27 smaller cubes of 1 cm side.
Let's consider the number of cubes with different number of painted faces:
1. Number of cubes with 0 painted faces:
As the given cube is painted on all its faces, there won't be any cube with 0 painted faces.
2. Number of cubes with 1 painted face:
Each face of the given cube is painted, so the cubes with 1 painted face will be the ones that have an edge on any of the faces of the given cube. So, there will be 12 such cubes.
3. Number of cubes with 2 painted faces:
The cubes with 2 painted faces will be the ones that have two of their faces on the adjacent edges of the given cube. So, there will be 6 such cubes.
4. Number of cubes with 3 painted faces:
Each corner of the given cube will have three of its faces painted, so there will be 8 such cubes.
5. Number of cubes with 4 painted faces:
In the given cube, the center cube will have all its faces painted, so there will be only one cube with 4 painted faces.
6. Number of cubes with 5 painted faces:
As there are no cubes with 0 painted faces, there won't be any cube with 5 painted faces.
7. Number of cubes with 6 painted faces:
As there are no cubes with 0 painted faces, there won't be any cube with 6 painted faces.
Therefore, the total number of cubes with exactly 2 painted faces will be 6. Hence, the correct option is (d) 12.
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Community Answer
A solid cube of 3 cm side, painted on all its faces, is cut up into sm...
In my opinion answer must be b 8 u can imagine room in which u r sitting a cube of side 3 now divide into 27 cubes as of side 1 now just cube at middle corner of the room has exactly 2 side painted so 8 should be answere rest u decide and respond
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A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces?a)12b)8c)6d)4Correct answer is option 'D'. Can you explain this answer?
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