Question

If the areas of three adjacent faces of a cuboid are $X,Y$ and $Z$ respectively, then find the volume of a cuboid.

Answer 1

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

Volume of cuboid $abc$

$X=ab,Y=bc,Z=ca$

Consider $XYZ=\left(ab\right)\left(bc\right)\left(ac\right)$

$XYZ=(abc{)}^2$

$⟹abc=\sqrt{XYZ}$

So the Volume of Cuboid is $\sqrt{XYZ}$