Question

Find the volume of a cuboid having surface areas of three adjacent faces as $x,y$ and $z$.

Answer 1

Let the sides of the cuboid be $a,b$ & $c$.

Given $x,y$ & $z$ are areas of $3$ adjacent faces of the cuboid.

Hence $x=ab,y=bc,z=ca$

$\left(x\right)\left(y\right)\left(z\right)=\left(ab\right)\left(bc\right)\left(ca\right)$

$xyz=(abc{)}^2\Rightarrow abc=\sqrt{xyz}$

$\therefore$ volume of cuboid $=\sqrt{xyz}$