The diagonal of a cube measures 8√3 cm. Find its total surface area in ${\text{cm}}^2$.

For a cube of edge a the space diagonal is a√3, so a√3 = 8√3 gives $a=8$ cm. Total surface area = $6a^2=6\times 64=384{\text{cm}}^2$. (512 is the volume in ${\text{cm}}^3$, not an area; treating 8√3 itself as the edge gives $a^2=192$ and a wrong $1152{\text{cm}}^2.$)