The sum of the lengths of all 12 edges of a cube is 84 cm. Find the volume of the cube.

Step-by-step solution

1. The sum of all edges of a cube is $12a$, where $a$ is the edge length.
2. Set $12a=84$ and solve for $a$: $a=84/12=7\text{cm}$.
3. Volume of a cube is $V=a^3$.
4. Compute $V=7^3=343$ cm³.
5. Therefore, the volume is $343$ cm³.

Concept tested: Volume from sum of edges

Published 13 October 2026 · How this solution was prepared and checked