A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, then find the edge of the third smaller cube.

Edge of the cube before melting = $$12\ cm$$

Volume of this cube $$(V)= 12^{3} = 1728\ cm$$

Volume of two smaller cubes will be $$6^{3}$$ and $$8^{3}$$ respectively i.e 

Volume of first smaller cube $$(V1) = 216\ cm$$; 

Volume of second smaller cube $$(V2)= 512\ cm$$

As the bigger cube is melted into three smaller cubes. The volume of the bigger cube is equal to volume of the smaller cubes taken together.

$$V = V1 + V2 + V3$$

$$1728 = 216 + 512 + V3\ (or)\ V3 = 1000$$

Now edge of the third smaller cube = $$\sqrt[3]{1000} = 10$$.

Hence, option A is the correct answer.