Question

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that $V^2=xyz.$

Answer 1

Let the dimensions of the cuboid be a, b and c.

x = ab, y = bc, z = ca

and V = abc

Now L.H.S. = $V^2$

$=(abc{)}^2=a^2{b}^2{c}^2$

$=ab.bc.ca$

$=xyz=R.H.S$

Hence $V^2=xyz$