Question

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is ______.

विकल्प

• 12 cm

• 24 cm

• 18 cm

• 20 cm

Answer 1

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is 12 cm.

Explanation:

The edges of three cubes are 6 cm, 8 cm and 10 cm, respectively.

∴ Sum of volumes of the three metal cubes

= 6³ + 8³ + 10³  ...[∵ Volume of cube = (edge)³]

= 216 + 512 + 1000

= 1728 cm³

Since, a new cube is formed by melting these three cubes.

Let a be the side of new cube. Then,

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

⇒ a³ = 1728

∴ a = 12 cm

Hence, the edge of the new cube is 12 cm.