A cube has a total surface area of $384{\text{ cm}}^2$. Which of the following is its volume?

Step-by-step solution

1. 1. Use the formula for the surface area of a cube: $S=6a^2$ where $a$ is the side length.
2. 2. Set up the equation $6a^2=384$ and solve for $a^2$: $a^2=\frac{384}{6}=64$.
3. 3. Find the side length: $a=\sqrt{64}=8\text{ cm}$.
4. 4. Compute the volume using $V=a^3$: $V=8^3=512{\text{ cm}}^3$.
5. 5. The volume matches option (A) 512 cm${}^3$.
6. 6. Therefore, the correct answer is 512 cm${}^3$.

Concept tested: Cube surface area and volume

Published 16 October 2026 · How this solution was prepared and checked