Question

The areas of three adjacent faces of a cuboid are x, y, and z. If the volume is V, prove that V2 = xyz.

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Answer 1

Step-by-step explanation:

V = l×b×h

area of 3 adjacent faces=lb×bh×lh

=l×l×b×b×h×h

which is equal to square of V

Answer 2

Answer:

v² = xyz  

Step-by-step explanation:

we assume that the dimensions of cuboid are l, b, h  as for length, breadth and height

according to the question,

area of three faces x, y and z

l × b = x--(1)

b × h = y---(2)

l × h = z---(3)

on multiplying (1 ),(2) and (3) we have

lb × bh × lh = xyz

l²×b²×h² = xyz

(lbh)² = xyz

∴ v² = xyz                 (∵ volume of the cuboid= v = lbh)

hope it helps!