A cube is to be cut into 8 pieces of equal size and shape. Here, each cut…
2024
A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube.
The minimum number of such cuts required is
- A.
3
- B.
4
- C.
7
- D.
8
Attempted by 57 students.
Show answer & explanation
Correct answer: A
Key idea: use three perpendicular full cuts through the center to produce eight equal smaller cubes.
First cut: make a straight planar cut through the center parallel to one pair of faces. This divides the cube into 2 equal rectangular solids.
Second cut: make a straight planar cut perpendicular to the first and through the center. This yields 4 equal pieces.
Third cut: make a straight planar cut perpendicular to the first two and through the center. This produces 8 equal smaller cubes.
Why fewer cuts won't work: with two full straight cuts the maximum number of equal pieces you can get (while keeping them identical in size and shape) is four, so a third cut is necessary to reach eight.
Conclusion: The minimum number of full straight cuts required is 3.
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