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:

For dividing a cube into \(2^n\) smaller cubes, the minimum number of cuts required is \(n\), one cut along each dimension (length, breadth, and height).

Answer 1

The Correct Option is A

To divide a cube into \(8\) equal parts (smaller cubes), the cube must be cut along its three dimensions: length, breadth, and height. Step 1: First Cut (Lengthwise)
The first cut divides the cube into \(2\) equal parts along its length. Step 2: Second Cut (Breadthwise)
The second cut divides each of the \(2\) parts into \(2\) smaller parts, making a total of \(4\) parts. Step 3: Third Cut (Heightwise)
The third cut divides each of the \(4\) parts into \(2\), resulting in \(8\) smaller cubes. Thus, a total of \(3\) cuts are required to divide the cube into \(8\) equal pieces. Final Answer: \[ \boxed{3} \]