Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. The surface area of new cube is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 486 cm2
When solids 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 its surface area from the side.
Total volume: \(1^{3}+6^{3}+8^{3}=1+216+512=729\) cm3
Side of the new cube: \(\sqrt[3]{729}=9\) cm, since \(9\times9\times9=729\)
Surface area of a cube is \(6a^{2}\): \(6\times9^{2}=6\times81=486\) cm2