Cube from space diagonal: The space diagonal of a cube is 8√3 cm. Find the total surface area of the cube (in cm2).

Introduction / Context:The problem links a cube’s space diagonal to its edge length and then asks for surface area. This is a direct application of the cube diagonal relation and the surface area formula.

Given Data / Assumptions:

• Space diagonal d = 8√3 cm
• For a cube of edge a: d = a√3

Concept / Approach:

• Compute a from d = a√3.
• Surface area SA = 6 * a^2.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 512 cm2: Uses 8 faces or wrong formula.
• 192 cm2: Halves the correct value.
• 786 cm2: Arbitrary, not from standard formula.

Common Pitfalls:

• Confusing space diagonal with face diagonal (face diagonal = a√2).
• Forgetting to square a when computing SA.

Final Answer:

384 cm2