Question

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

Answer 1

Let the 3 dimensions of the cuboid be l,b and h

So,

$x=lb$

$y=bh$

$z=hl$

multiplying above three equations,

$\begin{array}{c}xyz=lb\times bh\times hl\\ =l^2{b}^2{h}^2\end{array}$

As,

V=lbh

So,

$\begin{array}{c}{V}^2=l^2{b}^2{h}^2\\ V^2=xyz\end{array}$

Hence Proved