The surface areas of the three co-terminus faces of a cuboid are $x, y$ and $z$ respectively. If $V$ be the volume of the cuboid, then $V^{2} = x y z$

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Solution

The three co-terminus faces of the cuboid are rectangular with dimensions $(l, b), (b, h), (h, l)$
$∴$ $x = l \times b$ ; $y = b \times h$ ; $z = l \times h$
$∴ x y z = l^{2} \times b^{2} \times h^{2} = {(l \times b \times h)}^{2}$
$= V^{2} (∵ V = l \times b \times h)$
$V^{2} = x y z$

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