Question

Area of three sides of a cuboid are A,B,C respectively. find Volume

Answer 1

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...
$V = \sqrt{ABC}$