Three solid iron cubes of edges 4 cm, 5 cm and 6 cm are melted together to make a new cube. 62 cm³ of the melted material is lost due to improper handling. The area (in cm²) of the whole surface of the newly formed cube is

Volume of all three cube
= 4³ + 5³ + 6³
= 64 + 125 + 216
= 405 cm³
Now, 62 cm³ is lost due to improper handling.
∴ Volume of new cube
= 405 - 62
= 343
(Side of new cube)³ = 343
Side of new cube $$ = \root 3 \of {343} = 7$$
Total surface area of new cube
= 6 × (side)²
= 6 × (7)²
= 6 × 49
= 294 cm²