Question

the three adjacent faces of a cube is x,y,z and its volume is

Answer 1

Let the sides of the cube be a.
Given x, y and z are areas of three adjacent faces of the cuboid Hence x=a2,  y=a2, z=a2
 (x)(y)(z) = (a2)(a2(a2) 
xyz= (a3)2 a3 = √xyz Thus the volume of cuboid, V= a3 = √xyz
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Answer 2

Answer:

Let the 3 dimensions of the cuboid be l,b and h

So,

x=lb

y=bh

z=hl

multiplying above three equations,

xyz=lb×bh×hl

=l  

2

b  

2

h  

2

 

​  

 

As,

V=lbh

So,

V  

2

=l  

2

b  

2

h  

2

 

V  

2

=xyz

​  

 

Hence Proved