Three solid cubes of metal have sides 6 cm, 8 cm and 10 cm, respectively. They are melted to form a new cube. What is the surface area of this new cube?

Volume of the first cube = 6³ = 216 cm³ Volume of the second cube = 8³ = 512 cm³ Volume of the third cube = 10³ = 1000 cm³ Total volume = 216 + 512 + 1000 ⇒ Total volume = 1728 cm³ Let the side of the new cube be x cm. Volume of the new cube = x³ Since the volume of the new cube is equal to the total volume of the three cubes: x³ = 1728 ⇒ x = 12 cm Surface area of the new cube = 6 × 12² ⇒ Surface area = 6 × 144 ⇒ Surface area = 864 cm² The surface area of the new cube is 864 cm².