The areas of three adjacent faces of a cuboid are x,y,z .the volume is V ,prove that V square = xyz

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Solution

Let the sides of the cuboid be a, b and c.
Given x, y and z are areas of three adjacent faces of the cuboid
Hence x=ab, y=bc, z=ca
(x)(y)(z) = (ab)(bc)(ca)
xyz= (abc)2
abc = √xyz
Thus the volume of cuboid, V= abc = √xyz
Therefore V^2 = xyz

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