Question:
Two cubes, each of volume $512 \mathrm{~cm}^{3}$ are joined end to end. Find the surface area of the resulting cuboid.
Solution:
Given that,
Volume of the cube $=512 \mathrm{~cm}^{3}$
$\Rightarrow$ side $^{3}=512$
$\Rightarrow$ side $^{3}=8^{3}$
⇒ side = 8 cm
Dimensions of the new cuboid formed
Length (l) = 8 + 8 = 16 cm, Breadth (b) = 8 cm, Height (h) = 8 cm
Surface area = 2(lb + bh + hl)
= 2(16 * 8 + 8 * 8 + 16 * 8)
$=640 \mathrm{~cm}^{2}$
Therefore, Surface area is $640 \mathrm{~cm}^{2}$.
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