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.

• A. 284 cm²
• B. 286 cm²
• C. 296 cm²
• D. 280 cm²

Answer 1

The correct option is B

286 cm²

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 $c{m}^2$.

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 = $a^3$

⇒$a$ = 6 cm

Total Surface area of the cube is given by $6a^2$ = 6 × (6)² = 216 $c{m}^2$.

Hence, the difference between surface areas of two solids = (502 -216) $c{m}^2$ = 286 $c{m}^2$.