Cube with equal surface area and volume (numerically) — find edge length: If the numerical value of the volume (in unit^3) equals the numerical value of the surface area (in unit^2) of a cube, what is the edge length of the cube in units?

Introduction / Context:For a cube of edge a, the volume is a^3 and total surface area is 6a^2. The question states their numerical values are equal, which allows solving directly for a.

Given Data / Assumptions:

• Volume V = a^3
• Surface area S = 6a^2
• Numerical equality: a^3 = 6a^2 with a > 0

Concept / Approach:Divide both sides by a^2 (a ≠ 0) to isolate a.

Step-by-Step Solution:a^3 = 6a^2 ⇒ a = 6

Verification / Alternative check:Check: volume 216 and surface area 216 (units differ but numbers match) satisfies the condition.

Why Other Options Are Wrong:No other integer satisfies a^3 = 6a^2 for positive a.

Common Pitfalls:Treating units as needing to match; only numerical equality is required here.

Final Answer:6