Question

The areas of three adjacent faces of a
rectuargular box 2 a 2 b and 2c, Prove that v2=8abc

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Answer 1

Answer:

Let dimensions be x, y and z of box

Volume will be V = xyz

Given

xy = 2A

yz = 2B

zx = 2C

Multiply all three equations

\begin{gathered}(xy)(yz)(zx) = 8ABC (xyz) }^{2} = 8ABC {V}^{2} = 8ABC\\ V= 8ABC}

(xy)(yz)(zx)=8ABC

(xyz) =8ABC

V =8ABC

So Volume square is 8ABC