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

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 us consider, Areas of three faces of cuboid as x,y,z So, Let length of cuboid be = l Breadth of cuboid be = b Height of cuboid be = h Let, x = l×b y = b×h z = h×l Else we can write as xyz = l² b² h²….. (i) If ‘V’ is volume of cuboid = V = lbh V² = l² b² h² = xyz …… from (i) ∴ 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 us consider,

Areas of three faces of cuboid as x,y,z

So, Let length of cuboid be = l

Breadth of cuboid be = b

Height of cuboid be = h

Let, x = l×b

y = b×h

z = h×l

Else we can write as

xyz = l² b² h²….. (i)

If ‘V’ is volume of cuboid = V = lbh

V² = l² b² h² = xyz …… from (i)

∴ V² = xyz

Hence proved.