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

$x^{2} y^{2} z^{2}$

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$x y z$

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$x^{3} y^{3} z^{3}$

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$2 x y z$

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Solution

The correct option is B
$x y z$

Let $l, b, h$ be the length, breadth and height of the cuboid.

Volume, $V = l b h$
$∴$ Area of three adjacent faces
$\Rightarrow l b = x$ ... (i)
$\Rightarrow b h = y$ ... (ii)
$\Rightarrow h l = z$ ... (iii)
Multiplying (i), (ii) and (iii), we get
$l^{2} b^{2} h^{2} = x y z$
$\Rightarrow (l b h)^{2} = x y z$
$\Rightarrow V^{2} = x y z$

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