Question

If the areas of three adjacent faces of a cuboid are 8 ${cm}^2,$$18{cm}^2,$ and $25{cm}^2,$ Find the volume of the cuboid .

Answer 1

Given: $A_1=lb=8$sq.cm

$A_2=bh=18$sq.cm

$A_3=lh=25$sq.cm

$\Rightarrow lb\times bh\times lh=8\times 18\times 25$

$\Rightarrow {\left(lbh\right)}^2=2\times 2\times 2\times 3\times 3\times 2\times 5\times 5$

$\Rightarrow lbh=\sqrt{(2\times 2\times 2\times 3\times 3\times 2\times 5\times 5)}$

$\therefore lbh=2\times 2\times 3\times 5=60$cubic cm

$\therefore$ Volume of the cuboid$=lbh=60$cubic cm