Question

What is the maximum number of pieces into which a cube can be cut by 10 cuts.

• A. 125
• B. 80
• C. 100
• D. Cannot be determined

Hint:

Always try to make the numbers of cuts in each direction equal or differ by at most 1. For example, for 10 cuts: 3, 3, 4 is better than 2, 4, 4 ($3 \times 5 \times 5 = 75$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To maximize pieces from a given number of cuts, distribute the cuts as evenly as possible among the three axes.

Step 2: Key Formula or Approach:
Maximum Pieces = $(x+1)(y+1)(z+1)$, where $x+y+z = \text{Total Cuts}$.

Step 3: Detailed Explanation:
1. Total cuts = 10. 2. Distribute 10 into three numbers $x, y, z$ as evenly as possible: - $10 \div 3 = 3$ with a remainder of 1. - So, the cuts should be 3, 3, and 4 ($3+3+4 = 10$). 3. Number of pieces = $(3+1) \times (3+1) \times (4+1)$. 4. Calculation: $4 \times 4 \times 5 = 16 \times 5 = 80$.

Step 4: Final Answer:
The maximum number of pieces is 80.