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")`

Answer 1

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)`