The surface area of a cube is $150{\text{ cm}}^2$. Find the length of an edge of the cube and its volume.

Step-by-step solution

1. 1. For a cube, surface area $S=6a^2$, where $a$ is the edge length.
2. 2. Set $6a^2=150$ and solve for $a^2$: $a^2=150/6=25$.
3. 3. Take square root: $a=\sqrt{25}=5\text{ cm}$.
4. 4. Volume of a cube $V=a^3=5^3=125{\text{ cm}}^3$.

Concept tested: Cube surface area and volume

Published 10 October 2026 · How this solution was prepared and checked