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Let l,b,h be the length, breadth and height respectively
Let A = l * b
Thus l =  \frac{A}{b} ...(i)
Let B = b * h
Thus b =  \frac{B}{h} ...(ii)
Let C = h * l
Thus h =  \frac{C}{l} ...(iii)

We know Volume (V) = l*b*h
Replacing l,b&h usin (i),(ii)&(iii) we get...
V= \frac{A}{b}* \frac{B}{h}* \frac{C}{l}

Further simplifiying we get...
V= \frac{ABC}{lbh} ...(iv)
but lbh=V
Thus eq.(iv) becomes
V= \frac{ABC}{V}
Thus simplyfing we get...
V =  \sqrt{ABC}
2 5 2
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