For a cube, suppose the numerical value of its volume equals the numerical sum of all its edges. Find the total surface area (square units).

Introduction / Context:
This functional condition equates a^3 (volume) to 12a (sum of edges) for a cube with edge a. Solving the resulting equation determines a, then the total surface area 6a^2 is immediate. It practices translating a verbal condition into algebra and following through with correct power handling.

Given Data / Assumptions:

• Volume V = a^3.
• Sum of edges = 12a.
• Equation: a^3 = 12a with a > 0 (physical edge).

Concept / Approach:
Divide both sides by a (a ≠ 0) to get a^2 = 12. Then compute S = 6a^2 directly from this value without first extracting a, which avoids radicals in the surface area.

Step-by-Step Solution:
a^3 = 12a ⇒ a^2 = 12S = 6a^2 = 6 * 12 = 72 (square units)

Verification / Alternative check:
If desired, a = √12 = 2√3; then V = (2√3)^3 = 8 * 3√3 = 24√3 and 12a = 24√3 match numerically, consistent with the condition.

Why Other Options Are Wrong:
12 and 36 are too small (correspond to using a or a^2 directly); 144 doubles the correct surface area.

Common Pitfalls:
Cancelling by a when a = 0 (edge cannot be zero); computing surface area as 6a instead of 6a^2.

Final Answer:
72