Three cubes of sides 8 cm, 6 cm and 1 cm are melted to form a new cube. The surface area of the cube so formed is __________.

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Solution

Let the edge of new cube be a cm.

The sides of the three cubes are 8 cm, 6 cm and 1 cm.

It is given that, the three cubes are melted to form the new cube.

∴ Volume of the new cube = Sum of volumes of the three cubes

⇒ a³ = (8 cm)³ + (6 cm)³ + (1 cm)³ [Volume of cube = (Side)³]

⇒ a³ = 512 + 216 + 1 = 729 cm³

⇒ a³ = (9 cm)³

⇒ a = 9 cm

∴ Surface area of the new cube = 6a² = 6 × (9 cm)² = 6 × 81 cm² = 486 cm²

Thus, the surface area of the new cube is 486 cm².

Three cubes of sides 8 cm, 6 cm and 1 cm are melted to form a new cube. The surface area of the cube so formed is _486 cm²__.

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