Question

The area of three adjacent faces of cuboid are $108{cm}^2,72{cm}^2$ and $96{cm}^2$ respectively. Find the volume of the cuboid.

Answer 1

$ab=108bc=72ca=96$

$b=\frac{108}{a}\frac{108}{a}.c=72\frac{2a}{3}\times a=96$

$b=\frac{108}{12}c=\frac{72a}{108}{a}^2=48\times 3$

$b=9c=\frac{72a}{108}{a}^2=144$

$c=\frac{6a}{9}=\frac{2a}{3}a=12$

$c=\frac{2}{3}\times 12$

$c=8$

Volume of cuboid$=abc=12\times 7\times 8=108\times 8=864$