Areas Of Three Adjacent Faces Of Cuboid

The areas of three adjacent faces of a cuboid are A1, A2, and A3 . If its volume is V, prove that V2 = A1. A2. A3

Answers:

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

∴ Volume = abc

Also, A₁ = ab, A₂ = bc , A₃ = ca

∴  A_1.A₂.A₃  = (ab)(bc)(ca)  = a² b² c² = (abc)² = V²

⇒  V²  =  A_1.A₂.A₃