Three solid metal cubes of edges 6 cm, 8 cm and 10 cm are melted together and recast as a single cube. Find the surface area of the new cube in ${\text{cm}}^2$.

Total volume $=216+512+1000=1728{\text{cm}}^3$, so the new edge = ∛1728 = 12 cm and its surface area = $6\times 144=864{\text{cm}}^2$. (Adding the three old surface areas, $6(36+64+100)=1200{\text{cm}}^2$, is wrong — melting destroys surface, it does not preserve it; 1728 is the volume in ${\text{cm}}^3.$)