A solid metal cuboid of 343 cm $$\times$$ 49 cm $$\times$$ 7 cm is melted and cubes of edge 7 cm are formed. The sum of surface area (in cm$$^2$$) of the total number of cubes formed is:

A solid metal cuboid of 343 cm $$\times$$ 49 cm $$\times$$ 7 cm is melted and cubes of edge 7 cm are formed.

Here N = number of cubes formed from cuboid.

voume of cuboid = N $$\times$$ voume of cube

$$length\times breadth\times height=N\times\left(side\right)^3$$

$$343\times49\times7=N\times\left(7\right)^3$$

$$343\times49\times7=N\times343$$

$$N = 49\times7$$

N = 343

The sum of surface area (in cm$$^2$$) of the total number of cubes formed = $$343\times6\times\left(side\right)^2$$

= $$343\times6\times\left(7\right)^2$$

= $$343\times6\times49$$

= 100842