The volume of a cube is 512 cm3. What is its total surface area?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 384 cm2
The side of a cube is the cube root of its volume, and its total surface area is 6 faces of side \(a\): \(6a^2\).
\(a^3=512\), so \(a=8\) cm
Total surface area \(=6\times8^2=6\times64=384\) cm2
Why the other options are incorrect
Option (1) 768 cm2 — Incorrect. This is twice the total surface area, \(12a^2\).
Option (2) 108 cm2 — Incorrect. This would be \(6a^2\) for a side of about 4.2 cm, not 8 cm.
Option (4) 576 cm2 — Incorrect. This is \(9a^2\); a cube has only 6 faces.