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, find the edge of third smaller cube.

Given,

Edge of largest cube = 12 cm

Edge of 1st smaller cube = 6 cm

Edge of 2nd smaller cube = 8 cm.

Let the edge of 3rd smaller cube = x cm

Calculating the volume of larger cube,

Volume = a³

= (12)³

= 1728 cm³.

Calculating the volume of smaller cubes,

Volume of 1st smaller cube = 6³ = 216 cm³.

Volume of 2nd smaller cube = 8³ = 512 cm³.

Volume of 3rd smaller cube = x³.

Since larger cube melts to form a smaller cubes,

∴ Volume of larger cube = Total volume of smaller cubes.

⇒ 1728 = 216 + 512 + x³

⇒ 1728 = 728 + x³

⇒ x³ = 1728 - 728

⇒ x³ = 1000

⇒ x = $\sqrt[3]{1000}$

⇒ x = 10 cm.

Hence, edge of third smaller cube = 10 cm.