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Mathematics

The edges of three cubes of metal are 3 cm, 4 cm and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube.

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Answer

Given:

Edges of three cubes:

Cube 1: s1 = 3 cm
Cube 2: s2 = 4 cm
Cube 3: s3 = 5 cm

Volume of new cube formed = Total volume of the 3 melted cubes

Let S be the edge of the new cube formed from the melted material.

Total Volume of the Three Cubes = V1 + V2 + V3

⇒ s13 + s23 + s33 = S3

⇒ 33 + 43 + 53 = S3

⇒ 27 + 64 + 125 = S3

⇒ S3 = 216

⇒ S = 2163\sqrt[3]{216}

⇒ S = 6 cm

Hence, the edge of the new cube is 6 cm.

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