Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. The surface area of the cube so formed is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 486 cm2
When the cubes are melted and recast, the amount of metal does not change, so the volume of the new cube is the sum of the three volumes. Its side follows from that volume, and the surface area of a cube is six times the area of one face.
Volume of the new cube: \(1^{3}+6^{3}+8^{3}=1+216+512=729\,\mathrm{cm^3}\)
Side: 9 cm, since \(9\times9\times9=729\)
Surface area: \(6\times9^{2}=6\times81=486\,\mathrm{cm^2}\)