Question

the area of three adjacent faces of cuboid are x, y, and z. if it's volume is v then prove that v square = xyz

Answer 1

x=l*w
y=w*h
z=l*h
$xyz= l^{2} w^2h^2=(lwh)^2$
But lwh=V
Therefore
$V^2=xyz$

Answer 2

let the dimensions of cuboid are
Length=l
breadth=b
height =h
given area of three faces x,y and z
lb= x--(1)
bh=y---(2)
lh= z---(3)
multiply (1),(2) and (3)
lb×bh×lh= xyz

l^2×b^2×h^2=xyz

(lbh)^2= xyz

v^2= xyz
since volume of the cuboid=v=lbh