A cube has total surface area 726 sq cm. Find the volume of the cube (in cubic centimetres).

Introduction / Context:
Surface area S and volume V of a cube depend on the edge a. From S = 6a^2 we can determine a exactly, and then compute V = a^3. This question tests careful algebra and unit handling from area to volume.

Given Data / Assumptions:

• S = 726 cm^2.
• S = 6a^2; V = a^3.

Concept / Approach:
Isolate a^2 = S/6, take its square root to get a, and then cube a. Numbers are chosen to yield an integer edge length.

Step-by-Step Solution:
a^2 = 726 / 6 = 121a = √121 = 11 cmV = a^3 = 11^3 = 1331 cm^3

Verification / Alternative check:
Recompute surface area from a = 11: S = 6 * 121 = 726 cm^2, confirming consistency.

Why Other Options Are Wrong:
Other values are not perfect cubes corresponding to a whole-number edge derived from 726/6 = 121.

Common Pitfalls:
Forgetting the square root; computing 726/6 incorrectly; or mixing units.

Final Answer:
1331 cm3