The areas of three adjacent faces of a cuboid are 18 $$cm^2$$, 20 $$cm^2$$ and 40 $$cm^2$$. What is the volume(in $$cm^3$$) of the cuboid?

The areas of three adjacent faces of a cuboid are 18 $$cm^2$$, 20 $$cm^2$$ and 40 $$cm^2$$.

Here L, B, and H are the length, breadth, and height of a cuboid respectively.

LB = 18    Eq.(i)

BH = 20    Eq.(ii)

LH = 40    Eq.(iii)

Volume of the cuboid = LBH

Square on the both of the sides.

$$\left(Volume\ of\ the\ cuboid\right)^2=L^2B^2H^2$$

Volume of the cuboid = $$\sqrt{\ LB\times\ BH\times\ LH}$$

= $$\sqrt{18 \times 20 \times 40}$$

= $$\sqrt{14400}$$

= 120 $$cm^3$$