# The Areas of Three Adjacent Faces of a Cuboid Are X, Y and Z. If the Volume is V, Prove that V^2 = Xyz - Mathematics

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that
V^2 = xyz

#### Solution

Let a, b, d be the length, breath and height of cuboid then,

x=ab
y=bd
z=da, and
v=abd                          [v=lxxbxxh]

⇒xyz=abxxbcxxca= (abc^2)

and v= abc

v^2=(abc)^2

v^2=xyz

Concept: Volume of a Cuboid
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Exercise 18.2 | Q 21 | Page 31

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