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 problems involving division of objects like cubes or cuboids, use the formula ( 2^n ), where ( n ) is the number of cuts, to calculate the resulting pieces.

Answer 1

The Correct Option is A

Step 1: Understanding the problem. To divide a cube into 8 equal parts, we need to make straight cuts. Each cut should divide the cube into smaller sections until 8 equal pieces are obtained.
Step 2: Visualizing the cuts. 1. Make the first cut along one plane (say the vertical plane) to divide the cube into 2 equal halves. 2. Make the second cut along a plane perpendicular to the first (say the horizontal plane) to divide each half into 2 more equal parts, resulting in 4 equal pieces. 3. Make the third cut along another perpendicular plane (say the depth plane) to divide each of the 4 parts into 2 more equal parts, resulting in 8 equal pieces.
Step 3: Verification. Each cut reaches the other end of the cube and divides it completely into smaller sections. After 3 cuts, we get ( 2^3 = 8 ) pieces, as required. Thus, the minimum number of cuts required is ( 3 ).