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

To solve this problem, we need to determine the minimum number of straight cuts required to divide a cube into 8 smaller cubes of equal size.

1. Understand the Initial Condition: We start with a single cube.
2. Creating the First Cut:
   • Make the first straight cut parallel to one of the faces of the cube. This cut divides the cube into 2 equal parts.
3. Creating the Second Cut:
   • Make the second cut perpendicular to the first one and parallel to another face of the cube, cutting through the previous two halves. This results in the formation of 4 equal smaller cubes.
4. Creating the Third Cut:
   • Finally, make the third cut perpendicular to the other two cuts and parallel to the remaining uncut face. This divides the 4 smaller cubes into 8 equal parts.

By examining each cut direction, we make sure effectively to divide all parts of the cube uniformly. This ensures an equal division of the initial cube into smaller ones.

Thus, the minimum number of cuts required to achieve 8 equal smaller cubes from a single cube is 3. This corresponds with the given correct answer option:

• 3

Therefore, the correct answer is 3.

Answer 2

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 \( \boxed{3} \).