Correct Option (2)
To obtain 64 identical pieces from a cube, the cube must be divided into 4 segments along each of its three dimensions (length, width, height), as 4 × 4 × 4 = 64.
To divide a dimension into 'n' segments, 'n-1' cuts are required. Therefore, to obtain 4 segments along one dimension, 4 - 1 = 3 cuts are needed.
Since this principle applies to all three orthogonal dimensions of the cube, the total minimum number of cuts required is the sum of cuts along each dimension: 3 (for length) + 3 (for width) + 3 (for height) = 9 cuts.
Incorrect Options:
Option 1 (8): This value is incorrect. It might arise from misinterpreting the relationship between the number of pieces and the number of cuts, or from an incorrect calculation of the cube root of 64, or by confusing the number of pieces with the number of cuts.
Option 3 (12): This value is incorrect. It could result from an error such as multiplying the number of segments along one dimension (4) by the number of dimensions (3), or by incorrectly assuming 4 cuts are needed per dimension (4 cuts × 3 dimensions = 12 cuts), rather than 3 cuts per dimension.
Option 4 (16): This value is incorrect. This option might stem from an incorrect calculation, such as considering only two dimensions (4 × 4 = 16 pieces on a face) or misapplying the number of segments per dimension to the total cuts required for the entire cube.