Question

The area of three adjacent faces of a cuboid are x,y,z .If the volume is v.prove thatv2=xyz

Answer 1

Let the dimensions of surface 1 be a and b 
such that area = ab=x
Let the dimensions of surface 1 be b and c
such that area = bc =y
Let the dimensions of surface 1 be c and a
such that area = ca =z
such that xyz=a^2 b^2 c^2        .....(i)

Volume of cuboid = product of sides= abc=v
squaring both sides 
v^2=a^2 b^2 c^2= xyz from equation (i)

Hence proved.

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