Question

Three cubes whose edges are $3$ cm, $4$ cm and $5$ cm, respectively are melted to from a single cube. Find the surface area of the new cube.

Answer 1

Let $x$ be the edge of the new cube

The volume of the new cube= Sum of the volumes of three cubes
$⟹x^3=3^3+4^3+5^3$
$=27+64+125$
$=216=6^3$
$⟹x=6$

Now, surface area of new cube $=6\times {\left(edge\right)}^2$
$=6\times 6\times 6$
$=216c{m}^2$