A cube has total surface area 6 square units. Find the volume of the cube (in cubic units).

Introduction / Context:
Surface area and volume of a cube are tied through the edge length a. Given the surface area, we first recover a from S = 6a^2 and then compute V = a^3. This reinforces correct manipulation of powers when moving between area (square units) and volume (cubic units).

Given Data / Assumptions:

• Total surface area S = 6 square units.
• Cube identities: S = 6a^2 and V = a^3.

Concept / Approach:
Solve a from S = 6a^2 → a^2 = S/6; take square root to get a; then raise a to the third power to get volume. No approximations are needed here because values are exact.

Step-by-Step Solution:
a^2 = 6 / 6 = 1a = √1 = 1V = a^3 = 1^3 = 1 cubic unit

Verification / Alternative check:
From a = 1, S = 6 * 1^2 = 6 confirms the premise; V = 1 is therefore correct.

Why Other Options Are Wrong:
2, 4, and 6 cubic units correspond to edges larger than 1 and would imply surface areas greater than 6.

Common Pitfalls:
Confusing S = 6a with S = 6a^2; skipping the square root step; or mixing up units.

Final Answer:
1 cu unit