Three metallic cubes whose sides are 6 cm, 8 cm and 10 cm respectively are melted and converted into a single cube. If there is no loss of metal in this process, then what is the length of the side of the new cube?

12 cm

We know that,

Volume of a cube = Side³

We have,

Three cubes of edges 6 cm, 8 cm and 10 cm

Volume of the new cube = Sum of the volumes of all the three smaller cubes 

= Sid ³ = 6³ + 8³ + 10³

= Side³ = 216 + 512 + 1000 

= Side³ = 1728

= Side= 12 cm