Question:
Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Solution:
Two cubes each of volume $512 \mathrm{~cm}^{3}$ are joined end to end.
Now, volume of a cube $=(\text { side })^{3}$
$\Rightarrow 512=(\text { side })^{3}$
$\Rightarrow$ Side of the cube $=\sqrt[3]{512}=8 \mathrm{~cm}$
If the cubes area joined side by side, then the length of the resulting cuboid is $2 \times 8 \mathrm{~cm}=16 \mathrm{~cm}$.
Breadth $=8 \mathrm{~cm}$
Height $=8 \mathrm{~cm}$
$\therefore$ Surface area of the cuboid $=2 \times($ length $\times$ breadth $+$ breadth $\times$ height $+$ length $\times$ height $)$
$=2 \times(16 \times 8+8 \times 8+16 \times 8)$
$=2 \times(128+64+128)$
$=640 \mathrm{~cm}^{2}$