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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:

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Solution

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+1,000
=1,728 cm3

Since a new cube is formed by melting these three cubes, the volume of the new cube formed is equal to the sum of the volume of the other cubes.
Let a be the side of new cube.
So, the volume of the cube formed = a3
Now, a3=1,728 cm3
a=12 cm
Hence, the edge of the new cube formed is 12 cm.

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