Two cubes, each of volume 512 cm


Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting cuboid.


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 $)$

$=2 \times(16 \times 8+8 \times 8+16 \times 8)$

$=2 \times(128+64+128)$

$=640 \mathrm{~cm}^{2}$

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