Given: areas of three adjacent faces of a cuboid are x, y, z respectively.

Let l, b, h be the length , breadth, height of the cuboid respectively.

∴ l × b = x – 1

b × h = y – 2

h × l = z – 3

Volume of the cuboid is: l × b × h

multiply eq’s –1, –2, –3

That is ,

l × b × b × h × l × h = x × y × z l² × b² × h²

⇒ l² × b² × h² = xyz

⇒ (l × b × h)² = xyz

⇒ (V)² = xyz (∵Volume of the cuboid is: l × b × h)

⇒ V = √xyz

∴ V = √xys

That is volume of the given Cuboid is : √xyz