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State true or false.

The areas of three adjacent faces of a cuboid are x, y, and z, then the volume of that cuboid is $V = x y z$ .

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True

False

answer is B.

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Detailed Solution

It is given that the areas of three adjacent faces of a cuboid are x, y and z.
Consider the length of the cuboid be l, the breadth be b, and the height be h.
Computing the value of faces in terms of l, b, h.

x = l b y = b h z = l h

Computing the formula of the volume of the cuboid,

V = l × b × h

Multiply x, y and z,

x y z = l b × b h × l h

Simplify the terms,

x y z = l 2 b 2 h 2 ⇒ x y z = l b h 2

Substitute the value of l, b and h from the equation

1

x y z = V 2

So, the given statement is false.
The correct statement should be that Volume,

V = x y z

Hence, option (2) is correct.

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