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

1.	The areas of three adjacent faces of a cuboid are x, y, and z. If the volumes is V, prove that V2 = xyz.
Answer» Given, Area of 3 adjacent faces of a cuboid = x, y, z V = volume of cuboid Let a, b, c are respectively length, breadth, height of each faces of cuboid So, x = ab = y = bc = z = ca V = abc Hence , xyz = ab × bc × ca = (abc)² = v² (v=abc) = v² = xyz Proved.

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

Answer»

Given,

Area of 3 adjacent faces of a cuboid = x, y, z

V = volume of cuboid

Let a, b, c are respectively length, breadth, height of each faces of cuboid

So, x = ab

= y = bc

= z = ca

V = abc

Hence , xyz = ab × bc × ca = (abc)² = v² (v=abc)

= v² = xyz Proved.