A cube has space diagonal 2√3 cm. Find the total surface area of the cube.

Introduction / Context:
The diagonal that joins two opposite vertices of a cube (space diagonal) relates directly to its edge length. Once the edge is known, the total surface area follows from a standard formula. This problem checks recall and correct use of cube identities without needing advanced geometry.

Given Data / Assumptions:

• Space diagonal d = 2√3 cm.
• For a cube of edge a: space diagonal d = a√3.
• Total surface area S = 6a^2.

Concept / Approach:
Invert the space-diagonal relation to find a = d/√3, then substitute into S = 6a^2 to get the surface area. Keep the expression exact; numbers are chosen so the radical cancels neatly.

Step-by-Step Solution:
a = d / √3 = (2√3) / √3 = 2 cmS = 6a^2 = 6 * 2^2 = 6 * 4 = 24 sq cm

Verification / Alternative check:
Rebuild the diagonal from a = 2: d = a√3 = 2√3 cm, matching the given. Therefore the derived surface area is consistent.

Why Other Options Are Wrong:
15, 18, and 25 sq cm do not equal 6a^2 with a = 2. They arise if one confuses face area (a^2 = 4) or misapplies constants (e.g., 4a^2 = 16). Only 24 sq cm fits the cube identity.

Common Pitfalls:
Using the face diagonal formula a√2 instead of the space diagonal a√3; forgetting to square a in S = 6a^2; or rounding radicals prematurely.

Final Answer:
24 sq cm