Question

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. Then, find the difference between total surface areas of the two solids.

Answer 1

The metal sheet is in the shape of a cuboid.
Total surface area of the cuboid $=2(lb+bh+hl)=2\left[\right(27\times 8)+(8\times 1)+(1\times 27\left)\right]=502c{m}^2$

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

$27\times 8\times 1=a^3$

$a$ = 6 cm

Total Surface area of the cube = $6a^2=6\times (6{)}^2=216c{m}^2$

The difference between surface areas of two solids = 502 -216 = 286 $c{m}^2$.