Question

Three cubes whose edges measure $3cm,4cm$ and $5cm$ respectively are used to form a single cube. Find its edge. Also, find the surface area of the new cube.

Answer 1

Let $x$ cm be the edge of the new cube.

Then, the volume of the new cube$=$ Sum of the volumes of three cubes

$\Rightarrow x^3=3^3+4^3+5^3=216$

$\Rightarrow x^3=6^3\Rightarrow x=6cm$

The edge of the new cube is $6cm$ long.

Surface area of the new cube$=6x^2=6\times 6^2{cm}^2=216{cm}^2$