Three cubes of edges $6\text{cm}$, $8\text{cm}$ and $10\text{cm}$ are melted without loss of metal into a single cube. The edge of the new cube will be:

When the three smaller metal cubes are melted down and recast into a single larger cube, the total volume remains conserved.
1. Volume of a cube is given by the formula:

$$V={\text{edge}}^3$$

2. **Sum of the volumes of the three smaller cubes ($V_{\text{total}}$):**

$$V_1=6^3=216{\text{cm}}^3$$

$$V_2=8^3=512{\text{cm}}^3$$

$$V_3=10^3=1000{\text{cm}}^3$$

$$V_{\text{total}}=216+512+1000=1728{\text{cm}}^3$$

3. **Finding the edge of the newly formed single cube ($a$):**

$$a^3=V_{\text{total}}=1728$$

$$a=\sqrt[3]{1728}=12\text{cm}$$

Therefore, the edge of the new larger cube is $12\text{cm}$.