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Question

If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is
(a) xyz
(b) 2xyz
(c) xyz
(d) 3xyz

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Solution

(c) xyz
Let the length of the cuboid = l
breadth of the cuboid = b
and height of the cuboid = h
Since, the areas of the three adjacent faces are x, y and z, we have:

lb=xbh=ylh=z

Therefore,

lb×bh×lh=xyzl2b2h2=xyzlbh=xyz

Hence, the volume of the cuboid = lbh=xyz.

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