Question

Areas of the three adjecent faces of cuboid are A, B and C square units respectively
and its volume is V cubic units. Prove that V2 = ABC.​

Answer 1

Answer:

Area of A= b×h

Area of B= l×b

Area of C=l×h

Volume=l×b×h

(multiplying by Volume)

Volume×volume=(l×b×h)(l×b×h)

2V=(B×h)(l×A)

2V=B×l×A×h

2V=A×B×l×h

2V=A×B×C

2V=ABC

Step-by-step explanation:

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Answer 2

lets assume that the sides of cuboid is a, b and c respectively the area of the adjacent faces are A, B and C so

a*b =A -----------eq1

a*c =C -------------------eq2

b*c =B -------------------eq3

and

volume of cuboid is = a*b*c ------------------eq4

given that volume of cuboid is V

so

V = a*b*c ------------------eq5

from eq 1,2,3

a*b*b*c*a*c = A*B*C

=>a*a*b*b*c*c= A*B*C

=> (a*b*c)^2=A*B*C

using eq5

=> (V)^2 = A*B*C

hence proved