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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 ______.
Options
xyz
2xyz
`sqrt("xyz")`
`root(3)("xyz")`
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Solution
If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is `underline(sqrt("xyz"))`.
Explanation:
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,
and z, we have:
lb = x
bh = y
lh = z
Therefore,
lb × bh × lh = xyz
⇒ l2 b2 h2 = xyz
⇒ lbh = `sqrt(xyx)`
Hence, the volume of the cuboid = lbh = `sqrt(xyz)`
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