Question

The dimensions of a metallic cuboid are $100$ cm $\times$ $40$ cm $\times$ $54$ cm. It is melted and recast into a cube. Find the surface area of cube.

Answer 1

Volume of the metallic cuboid
$=100$ $\times$ $40$ $\times$ $54$ $c{m}^3$
$=216000$ $c{m}^3$
Since the metallic cuboid is melted and is recast into a cube, the volume of the metallic = volume of the cube. Let the length of each edge of the recast cube be a cm, then,
Volume of the cube = Volume of the cuboid
$\Rightarrow$ $a^3=216000$
$\Rightarrow$ $a^3=6^3\times {10}^3$
$\Rightarrow$ $a=6\times 10=60cm$