Q.9 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
Why 3 Cuts Work
A single straight cut through the cube’s center along one dimension (say, length) divides it into 2 equal parts. The second cut, perpendicular to the first along the breadth, slices both parts into 4 equal pieces. The third cut, perpendicular to both along the height, divides those 4 into 8 identical smaller cubes.
Mathematically, each cut doubles the pieces when orthogonal: 1→2→4→8 (or 23=8). No rearrangement is needed; cuts stay on the intact cube.
Step-by-Step: How 3 Cuts Create 8 Cubes
- Cut 1 (X-axis): Slice midway parallel to one face—yields 2 halves.
- Cut 2 (Y-axis): Perpendicular midway—splits into 4 quarters.
- Cut 3 (Z-axis): Perpendicular midway—creates 8 small cubes.
Visualize: Each orthogonal cut multiplies pieces by 2, hitting 23=8. No stacking allowed per problem rules.
Option Analysis
| Option | Cuts Description | Pieces | Why Wrong |
|---|---|---|---|
| (A) 3 | One cut per dimension (x, y, z axes) | 8 cubes | Correct, as 2×2×2=8 |
| (B) 4 | Extra parallel cut | 5 slabs | Not cubes |
| (C) 7 | Separate after each: 1+2+4 | 8 cubes | Breaks “no stop” rule |
| (D) 8 | Cut each final cube | 8 | Inefficient |
Pro Tip
For n3 cubes, minimum cuts = 3(n−1). Here, n=2, so 3 cuts.
Master cube into 8 pieces minimum cuts for exams—practice variations like 27 cubes (6 cuts). Share if this cleared your doubt!
