A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. Find the difference between the surface areas (in cm2) of the two solids.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 286
When a solid is melted and recast, its volume stays the same, so the volume of the sheet gives the edge of the cube. The surface areas are then compared.
The cube (same volume as the sheet):
Volume of the sheet \(=27\times8\times1=216\) cm3
Edge of the cube \(=\sqrt[3]{216}=6\) cm
The surface areas:
Sheet (a cuboid): \(2(lb+bh+hl)=2(216+8+27)=502\) cm2
Cube: \(6a^{2}=6\times36=216\) cm2
Difference \(=502-216=\) 286 cm2