Question

If the area of three adjacent faces of a cuboid are x, y & z then prove that volume of cuboid, V = √xyz

Answer 1

Answer:

Step-by-step explanation:

Let say sides of cuboids are a , b & c

x = ab

y = bc

z = ca

xyz = (ab)(bc)(ca) = (abc)^2

√xyz  = abc

Volume of cube V = abc  

√xyz = V

QED

Answer 2

Step-by-step explanation:

- 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