All questions of Cubes and Dice for Class 6 Exam

Understanding Cube Cuts
To determine the maximum number of identical pieces a cube can be divided into by 7 cuts, we can follow a systematic approach. Each cut can increase the number of pieces exponentially, depending on how they intersect.
Maximum Pieces Formula
The formula to calculate the maximum number of pieces (P) created by n cuts is:
P = (n^3 + 5n + 6) / 6
This formula arises from the general principle of how each new cut can potentially intersect all previous cuts.
Calculating for 7 Cuts
Now, substituting n = 7 into the formula:
- P = (7^3 + 5*7 + 6) / 6
- P = (343 + 35 + 6) / 6
- P = 384 / 6
- P = 64
However, this result is for the maximum number of pieces resulting from 7 cuts, leading us to a misunderstanding.
Correct Approach for Identical Pieces
For identical pieces, we must consider how cuts can be made uniformly. To achieve the maximum number of identical pieces, we can divide the cube into smaller cubical units.
- Each cut can effectively divide the cube into smaller cubes.
- The best configuration involves making equal cuts along each dimension (length, width, height).
Identical Pieces Calculation
1. Making 3 Cuts in One Direction: This divides the cube into 4 pieces along that dimension.
2. Making 2 Cuts in the Second Direction: This divides the remaining pieces further, doubling the count.
3. Making 2 Cuts in the Third Direction: This again doubles the count.
Thus, the total number of pieces can be calculated as:
- 4 pieces (from first cuts) x 3 pieces (from second cuts) x 3 pieces (from third cuts) = 36 identical pieces.
Conclusion
Therefore, the correct answer for the maximum number of identical pieces a cube can be cut into by 7 cuts is 36, which corresponds to option 'B'.