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

Question

The areas of three adjacent faces of a cuboid are x, y, and z. If the volumes is V , prove that V 2 = xyz.

Philoid · Accepted 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.