A metal cube of edge 12 cm is melted and formed into three smaller cubes.

Let the edge of the third cube be $\mathrm{x} \mathrm{cm}$.

Three small cubes are formed by melting the cube of edge $12 \mathrm{~cm}$.

Edges of two small cubes are $6 \mathrm{~cm}$ and $8 \mathrm{~cm}$.

Now, volume of a cube $=(\text { side })^{3}$

Volume of the big cube $=$ sum of the volumes of the three small cubes

$\Rightarrow(12)^{3}=(6)^{3}+(8)^{3}+(\mathrm{x})^{3}$

$\Rightarrow 1728=216+512+\mathrm{x}^{3}$

$\Rightarrow \mathrm{x}^{3}=1728-728=1000$

$\Rightarrow \mathrm{x}=\sqrt[3]{1000}=10 \mathrm{~cm}$

$\therefore$ The edge of the third cube is $10 \mathrm{~cm}$.