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A cube of side n is painted green on all its sides. It is then cut into n3 identical cubes. How many of the smaller cubes will have three of its sides painted?
- a)4
- b)6
- c)8
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A cube of side n is painted green on all its sides. It is then cut int...
Since, all the sides of the cube is painted, the cubes cut out from the corners will have three of its faces green. Since there are 8 corners for a cube, there will be 8 such cubes.
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A cube of side n is painted green on all its sides. It is then cut int...
Understanding the Problem
When a cube of side n is painted on all sides and then cut into n³ identical smaller cubes, we need to determine how many of these smaller cubes will have three of their sides painted.
Key Observations
- The cubes with three painted sides are located at the corners of the larger cube.
- A cube has eight corners.
Location of Painted Smaller Cubes
- Each corner of the cube will correspond to one smaller cube after cutting.
- Since each corner contributes to a smaller cube, the total number of smaller cubes with three painted sides is equal to the number of corners.
Conclusion
- Therefore, regardless of the value of n (as long as n ≥ 2), there will always be 8 smaller cubes that have three of their sides painted.
- The correct answer is option 'C' - 8.
Final Thoughts
- This logical deduction helps in visualizing how painting and cutting a cube affects the smaller cubes.
- Always remember that the corners are the only places where three painted sides can occur after the cube is divided.
When a cube of side n is painted on all sides and then cut into n³ identical smaller cubes, we need to determine how many of these smaller cubes will have three of their sides painted.
Key Observations
- The cubes with three painted sides are located at the corners of the larger cube.
- A cube has eight corners.
Location of Painted Smaller Cubes
- Each corner of the cube will correspond to one smaller cube after cutting.
- Since each corner contributes to a smaller cube, the total number of smaller cubes with three painted sides is equal to the number of corners.
Conclusion
- Therefore, regardless of the value of n (as long as n ≥ 2), there will always be 8 smaller cubes that have three of their sides painted.
- The correct answer is option 'C' - 8.
Final Thoughts
- This logical deduction helps in visualizing how painting and cutting a cube affects the smaller cubes.
- Always remember that the corners are the only places where three painted sides can occur after the cube is divided.
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A cube of side n is painted green on all its sides. It is then cut into n3identical cubes. How many of the smaller cubes will have three of its sides painted?a)4b)6c)8d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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A cube of side n is painted green on all its sides. It is then cut into n3identical cubes. How many of the smaller cubes will have three of its sides painted?a)4b)6c)8d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A cube of side n is painted green on all its sides. It is then cut into n3identical cubes. How many of the smaller cubes will have three of its sides painted?a)4b)6c)8d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A cube of side n is painted green on all its sides. It is then cut into n3identical cubes. How many of the smaller cubes will have three of its sides painted?a)4b)6c)8d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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