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