Two cubes each of volume $64 {c m}^{3}$ are joined end to end. Find the surface area and volume of the resulting cuboid.

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Solution

Let the length of each edge of the cube of volume $64 {c m}^{3}$ be $x$ cm.
then, volume $= 64 {c m}^{3}$
$\Rightarrow x^{3} = 4^{3} \Rightarrow x = 4 c m$

The dimensions of the cuboid so formed are
Length $= L = (4 + 4) = 8 c m$
Breadth $= b = 4 c m$
Height $= h = 4 c m$

Surface area of the cuboid $= 2 (8 \times 4 + 4 \times 4 + 8 \times 4) {c m}^{2} = 160 {c m}^{2}$

Volume of the cuboid $= l b h = 8 \times 4 \times 4 {c m}^{3} = 128 {c m}^{3}$

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