A solid metal cuboid of 343 cm × 49 cm × 7 cm is melted and cubes of edge 7 cm are formed. The sum of surface area (in cm ) of total number of cubes formed is:

100842

We know that,

Volume of cuboid = lbh

Volume of cube = side ³

Total surface area of cube = 6(side)²

We have,

Dimensions of cuboid = 343 cm × 49 cm × 7 cm

Edge of cube = 7 cm

Let the number of cubes = x

x × 7³ = 343 × 49 × 7

x = (343 × 343) × \(\frac{1}{343  }\)

x = 343

Total surface area of 343 cubes = 343 × 6 × 7 × 7 = 100842 cm²