Question:
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
Solution:
As, volume of a cube $=27 \mathrm{~cm}^{3}$
$\Rightarrow$ (edge) $^{3}=27$
$\Rightarrow$ edge $=\sqrt[3]{27}$
$\Rightarrow$ edge $=3 \mathrm{~cm}$
The length of the resulting cuboid, $l=3+3=6 \mathrm{~cm}$,
its breadth, $b=3 \mathrm{~cm}$ and its height, $h=3 \mathrm{~cm}$
Now, the surface area of the resulting cuboid $=2(l b+b h+h l)$
$=2(6 \times 3+3 \times 3+3 \times 6)$
$=2(18+9+18)$
$=2 \times 45$
$=90 \mathrm{~cm}^{2}$