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Question -

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2 = xyz.



Answer -

Let a, b, c are the dimensions of a cuboid then,
x = ab, y = bc, z = ca
and V = abc
Now L.H.S. = V2
= (abc)2 = a2b2c2
= ab.bc.ca = xyz = R.H.S.
Hence V2 = xyz

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