If $A_{1}, A_{2} a n d A_{3}$ denote the areas of three adjacent faces of a cuboid, then its volume is

$A_{1} A_{2} A_{3}$

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$2 A_{1} A_{2} A_{3}$

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$\sqrt{A_{1} A_{2} A_{3}}$

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$\sqrt[3]{A_{1} A_{2} A_{3}}$

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Solution

The correct option is C
$\sqrt{A_{1} A_{2} A_{3}}$

$Let l, b, h be the dimensions of the cuboid.$

$∴ A_{1} = l b, A_{2} = b h, A_{3} = h l$

$\Rightarrow A_{1} A_{2} A_{3} = l b . b h . h l = l^{2} b^{2} h^{2}$

$\Rightarrow l b h = \sqrt{A_{1} A_{2} A_{3}}$

$∴ V o l u m e = \sqrt{A_{1} A_{2} A_{3}}$

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Similar questions

\sqrt{A_{1} A_{2} A_{3}}

^{3} \sqrt{A_{1} A_{2} A_{3}}

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

\sqrt{x y z}

3 \sqrt{x y z}

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