Cube from total surface area

Text

A cube has total surface area $150$ cm$^2$. Find the edge, the volume and the space diagonal of the cube.

Solution

From the surface $6a^2=150\Rightarrow a^2=25\Rightarrow a=5$ cm. Volume: $V=a^3=125$ cm$^3$. Space diagonal: $d=a\sqrt3=5\sqrt3\approx8.66$ cm. $\boxed{a=5\ \text{cm};\ \ V=125\ \text{cm}^3;\ \ d=5\sqrt3\approx8.66\ \text{cm}}$