Mathematics
The areas of three adjacent faces of a cuboid are x, y and z sq. units. If the volume is V cubic units, prove that V2 = xyz.
Mensuration
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Answer
Let the dimensions of cuboid be,
Length = l
Breadth = b
Height = h
We know that,
Volume of cuboid (V) = l × b × h
Areas of three adjacent faces :
x = l × b
y = b × h
z = h × l
Multiplying these three areas :
xyz = (l × b) × (b × h) × (h × l)
xyz = l2 × b2 × h2
xyz = (l × b × h)2
Substituting the value of V = l × b × h
∴ xyz = V2.
Hence, proved that V2 = xyz.
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