Three cubes with edges 8 cm, 6 cm and 1 cm respectively are melted together and formed into a single cube. Find the total surface area of the new cube.

To find the total surface area of the new cube formed we first need to find its edge

Volume of cube = (edge)³

Volume of cube with edge 8 cm = 8³ = 512 cm³

Volume of cube with edge 6 cm = 6³ = 216 cm³

Volume of cube with edge 1 cm = 1³ = 1 cm³

Let the edge of new cube formed be ‘a’

Volume of new cube = a³

As the three cubes are melted and the new cube is formed

Volume of new cube = volume of all the three cubes

⇒ a³ = 512 + 216 + 1

⇒ a³ = 729

⇒ a = 9

Surface area of cube = 6 × (edge)²

⇒ surface area of new cube = 6 × a²

= 6 × 9²

= 6 × 81

= 486 cm²

Therefore, surface area of new cube is 486 cm²