Question

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

Answer 1

Let the dimensions of cuboid are

Length$=l$

Breath$=b$

Height$=h$

$\begin{array}{c}x=l\times b\\ y=b\times h\\ z=l\times h\end{array}$

$xyz=l^2{b}^2{h}^2$

$={\left(lbh\right)}^2$

Then,

$l\times b\times h=V$

Therefore,

$V^2=xyz$