The areas of three adjacent faces of a cuboid are x, y and z. If the v

1.	The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, Prove that V2 = xyz.
Answer» Let a, b and c be the length, breadth, and height of the cuboid. Then, x = ab, y = bc and z = ca [Since areas of three adjacent faces of a cuboid are x, y and z (Given)] And xyz = ab x bc x ca = (abc)² ……(1) We know, Volume of a cuboid ( V ) = abc …..(2) From equation (1) and (2), we have V² = xyz Hence proved.

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, Prove that V2 = xyz.

Answer»

Let a, b and c be the length, breadth, and height of the cuboid.

Then, x = ab, y = bc and z = ca [Since areas of three adjacent faces of a cuboid are x, y and z (Given)]

And xyz = ab x bc x ca = (abc)² ……(1)

We know, Volume of a cuboid ( V ) = abc …..(2)

From equation (1) and (2), we have

V² = xyz

Hence proved.