Question

If $A,B,C$ denote the area of the three conterminous faces of a rectangular solid and $V$ be its volume, then $V={\left(ABC\right)}^{1/2}$.

Answer 1

Let l,b,h be edges of the rectangular solid so that
A=lb, B=bh, and C=lh
Now $ABC=lb\times bh\times lh=l^2{b}^2{h}^2$
or $lbh={\left(ABC\right)}^{1/2}$
Thus volume $V={\left(ABC\right)}^{1/2}$
Hence proved