The areas of three adjacent faces of a cuboid are $x, y$ and $z .$ If the volume is $V;$ then $: V^{2} = x y z .$
If true answer is 1,else 0

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Solution

Consider a cuboid ABCDEFGH whose length is 'l', breadth is 'b' and height is 'h'.
The area of face ABCD(yellow) is x = lb
The area of face BCFG(blue) is y = bh
The area of face ABGH(pink) is z = lh
The volume of a cuboid is V = lbh
The product of the areas of the three faces = xyz = lb * bh * lh = $l^{2} b^{2} h^{2} = V^{2}$ .
Hence proved.

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