Longest pencil in a box (space diagonal): A rectangular box has dimensions 8 cm × 6 cm × 2 cm. What is the maximum length of a pencil that can fit inside it?

Introduction / Context:The longest object that fits inside a rectangular box equals its space diagonal. This tests 3D Pythagoras across three perpendicular edges.

Given Data / Assumptions:

• Dimensions: 8 cm, 6 cm, 2 cm
• Max length L = √(8^2 + 6^2 + 2^2)

Concept / Approach:

• Apply space diagonal formula for a cuboid.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 2√13 cm: Uses half the sum inside the root incorrectly.
• 2√14 cm: Incorrect decomposition.
• 10√2 cm: Corresponds to √(8^2 + 6^2) only, ignoring the 2 cm height.

Common Pitfalls:

• Using face diagonal instead of space diagonal.
• Arithmetic slips inside the square root.

Final Answer:

2 √26 cm