A rectangular box has internal dimensions 8 cm × 6 cm × 2 cm. Find the maximum length of a pencil that can fit inside (the space diagonal).

Introduction / Context:
The longest straight object that fits inside a rectangular box lies along its space diagonal. This diagonal is found via the 3D Pythagoras relation using the three mutually perpendicular edges. The result often simplifies to a scaled square root.

Given Data / Assumptions:

• a = 8 cm, b = 6 cm, c = 2 cm.
• Space diagonal d = √(a^2 + b^2 + c^2).

Concept / Approach:
Square each dimension, sum them, and take the square root. Factor the radicand if possible to a nice multiple.

Step-by-Step Solution:
d^2 = 8^2 + 6^2 + 2^2 = 64 + 36 + 4 = 104d = √104 = √(4 * 26) = 2√26 cm

Verification / Alternative check:
A face diagonal would be √(8^2 + 6^2) = 10 cm; including the third dimension 2 cm increases it appropriately to √104 ≈ 10.198, consistent.

Why Other Options Are Wrong:
2√13 and 2√14 correspond to smaller sums; 10√2 ≈ 14.14 cm exceeds what can fit given the edges.

Common Pitfalls:
Using a face diagonal instead of space diagonal; arithmetic errors in squaring/adding; forgetting to simplify the radical.

Final Answer:
2√26 cm