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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 areas of the two solids is ___cm2.


A

296

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B

286

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C

284

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D

280

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Solution

The correct option is B

286


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

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

Let the side of a cube be a.

Volume of the cuboid = Volume of the cube

27×8×1=a3

a = 6 cm

Total Surface area of the cube = 6a2=6×(6)2=216cm2

The difference between surface areas of two solids = 502 -216 = 286 cm2.


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