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

$\frac{x y}{z}$

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

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

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$x y z$

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Solution

The correct option is D
$x y z$

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

Given : $l b \times b h \times h l = x \times y \times z$

$\Rightarrow x y z = (l b h)^{2}$

Volume, $V = l \times b \times h$

$∴ V^{2} = (l b h)^{2} = x y z$

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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

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