Question

If the areas of three adjacent faces of a cuboid are 8 $c{m}^2,18c{m}^{2}and25c{m}^2$, Find the volume of the cuboid.

Answer 1

Let l, b, h ar the dimensions of the cuboid, then

$lb=8c{m}^2$

$bh=18c{m}^2$

$hl=25c{m}^2$

$\therefore Volume=lbh=\sqrt{(lbh{)}^2}$

$=\sqrt{lb\times bh\times hl}=\sqrt{8\times 18\times 25}c{m}^3$

$=\sqrt{3600}c{m}^3=60c{m}^3$