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Question

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between total surface area of the two solids is ______ cm2.

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Solution

The metal sheet is in the shape of a cuboid.
Total surface area of the cuboid is given by 2 (lb + bh + hl) = 2[(27 ×8) + (8 ×1) + (1 ×27)] = 502 cm2.

When the metal sheet is melted into a cube, then the volume of the metal sheet will be equal to the volume of the cube.
Hence, Volume of the cuboid = Volume of the cube

Let each side of the cube be a

Hence, 27 × 8 × 1 = a3

a = 6 cm

Total Surface area of the cube is given by 6a2 = 6 × (6)2 = 216 cm2.

Hence, the difference between surface areas of two solids = (502 -216) cm2 = 286 cm2.


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