A cube has total surface area 726 m^2. Find its volume in m^3.

Introduction / Context:
Given a cube’s total surface area S, find side a from S = 6a^2, then compute the volume V = a^3. This is the reverse of the previous problem type.

Given Data / Assumptions:

• S = 726 m^2.
• S = 6a^2 ⇒ a^2 = S/6.
• V = a^3.

Concept / Approach:
Compute a^2, then a, then a^3. The arithmetic is neat because 726/6 is a perfect square.

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

Verification / Alternative check:
Back-calc surface area: 6a^2 = 6 * 121 = 726 m^2, confirming a = 11 m.

Why Other Options Are Wrong:
Other numbers do not equal 11^3 and would correspond to non-integer sides or incorrect squares.

Common Pitfalls:
Taking a as 726/6 (forgetting the square root), or miscomputing 11^3.

Final Answer:
1331 m3