The areas of three adjacent faces of a cuboid are $x, y$ and $z .$ If the volume of the cuboid is $V$ , then $V^{2}$ is equal to

x y z

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x y + y z + z x

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(x y z)

^{2}

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\sqrt{x y z}

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Solution

The correct option is A ( $x y z$ )
Let the dimensions of cuboid has $l, b, h$
as length, breadth and height respectively.
Given, three adjacent faces of cuboid are $x, y$ and $z$ .
$\Rightarrow x = l b; y = l h; z = b h$
Since, volume $V = l b h$
Consider, $V^{2} = (l b h)^{2}$
$= (l b h) \times (l b h)$
$= l b \times l h \times b h$
$∴ V^{2} = x y z$

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