# The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V,

Question:

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

Solution:

Let a, b and d be the length, breadth, and height of the cuboid.

Then, x = ab

y = bc

z = ca

and V = abc [V = l * b * h]

$=x y z=a b^{*} b c^{*} c a=(a b c)^{2}$

and V = abc

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

Therefore, $\mathrm{V}^{2}=(\mathrm{xyz})$