A cuboid of dimensions 9 cm × 8 cm × 6 cm has twice the volume of a cube. Find the total surface area (in cm^2) of the cube.

Introduction / Context:Relate the cuboid’s volume to twice the cube’s volume, then solve for the cube’s edge and compute its total surface area (TSA = 6a^2).

Given Data / Assumptions:

• Cuboid: 9 × 8 × 6 cm ⇒ V_cuboid = 432 cm^3.
• V_cuboid = 2 × V_cube.

Concept / Approach:Find V_cube = 432/2 = 216 cm^3. Then a^3 = 216 ⇒ a = 6 cm. Compute TSA = 6a^2.

Step-by-Step Solution:

Verification / Alternative check:Check: cube volume 6^3 = 216; twice equals 432 (the cuboid’s volume).

Why Other Options Are Wrong:They are close numerically but not the exact TSA from a = 6 cm.

Common Pitfalls:Computing lateral area instead of total; arithmetic slips in squaring or cube root.

Final Answer:216 sq cm