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

x y

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x y z

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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 B $\sqrt{x y z}$
Let the length ,breadth and hight of the cuboid be $p, q, r$ Then,
$p q = x$
$q r = y$
$p r = z$
Multiplying all these three equations, give
$p^{2} q^{2} r^{2} = x y z$
Square-rooting both the sides give,
$p q r = \sqrt{x y z}$
$\Rightarrow$ volume of cuboid $= \sqrt{x y z}$

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