Question

The three adjacent faces of cuboid are A1,A2and A1.If volume is V then prove that V=√A1 A2 A3

Answer 1

$let \: the \: length \: width \: and \: height \: be \: l \: b \: and \: h \: respectively$
A1=l×b
A2=b×h
A3=h×l

volume of cuboid=lbh

$l = \frac{a1}{b} \\ b = \frac{a2}{h} \\ h = \frac{a3}{l} \\ put \: value \: of \: l \: b \: and \: h \: in \: volume \\ \\ v = \frac{a1}{b} \times \frac{a2}{h} \times \frac{a3}{l} \\ v \times (lbh) = a1 \times a2 \times a3 \\ {v}^{2} = a1 \times a2 \times a3 \\ v = \sqrt{a1 \times a2 \times a3}$


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