Question on surface area and volume of cuboid

Question

I came across a question:

The surface area of the six faces of a rectangular solid are 4, 4, 8, 8, 18 and 18 square cms. The volume of the solid, in cubic centimetres is __.

I can guess that 4 is $lb$, and 8 is $bh$, and 18 is $lh$. But now if I suppose that $b = 2$, then I get $l = 2$ but it makes $h = 9$ which makes $bh = (2)(9) = 18$ false.

Can anyone show a better working for this.

Thanks a lot.

Answer 1

We have, $(lb)(bh) = b^{2}(lh)$.
So, $4 * 8 = 18b^{2}$ from where we get $b= \frac {4}{3}$ cms
Therefore $l=3$ cms and $h=6$ cms.
So, volume = $lbh$ = $3 * \frac {4}{3} * 6$ = $24$ cubic cms.

Answer 2

We have $4 \cdot 8 \cdot 18 = lbbhlh$ or $576=l^2b^2h^2$. Taking square roots gives $lbh=24$.