The areas of three adjacent faces of a cuboid are x, y and z then the volume of the cuboid is

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xyz

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\sqrt{x y z}

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\sqrt[3]{x y z}

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Solution

The correct option is C $\sqrt{x y z}$
Let the sides of the cuboid be a, b and c.
Given x, y and z are areas of three adjacent faces of the cuboid
Hence x=ab, y=bc, z=ca
$∴ X \times y \times z = (a b) (b c) (c a)$
$x y z = (a b c)^{2}$
$\Rightarrow a b c = \sqrt{x y z}$
Thus the volume of cuboid $a b c = \sqrt{x y z}$

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