Question

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

Hint:

Remember: To divide a cube into \( n^3 \) smaller cubes, you need \( n-1 \) cuts along each of the 3 axes. For 8 pieces, \( n = 2 \), so only 3 cuts are required.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
We need to divide a cube into 8 smaller cubes, each of equal size and shape. A cube has 6 faces, 12 edges, and 8 vertices. We are to perform straight cuts that go from one end of the cube to the other, ensuring that each cut divides the cube into equal pieces.
Step 2: Dividing the cube using 3 cuts.
To divide the cube into 8 smaller cubes, consider the following approach:
- The first cut should divide the cube in half, cutting through the center along one axis. This gives 2 equal pieces.
- The second cut should divide each of the two pieces in half along a different axis. This results in 4 pieces.
- The third cut should divide each of the 4 pieces in half along the third axis, resulting in 8 smaller cubes.
Thus, 3 straight cuts are sufficient to divide the cube into 8 smaller cubes, each of equal size and shape.
Step 3: Conclusion.
The minimum number of cuts required to divide a cube into 8 equal pieces is 3. Therefore, the correct answer is \( \boxed{3} \).