a cuboid having surface areas of three adjacent faces as X Y and Z has a volume
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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
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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
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