Question

Segue a imagem da questão:

Answer 1

Resposta:

Explicação passo a passo:

$a=(x-1)$

$b=x$

$c=(x+1)$

$D=\sqrt{102}\:m$

$D=\sqrt{a^{2}+b^{2}+c^{2} }$

$\sqrt{102}=\sqrt{(x-1)^{2}+x^{2} +(x+1)^{2} }$

$Elevando\:os\:dois\:lados\:ao\:quadrado,\:as\:raizes\;desaparecem!$

$102=x^{2} -2x+1+x^{2} +x^{2} +2x+1$

$102=x^{2} +x^{2} +x^{2} -2x+2x+1+1$

$102=3x^{2} +2$

$3x^{2} +2=102$

$3x^{2} =102-2$

$3x^{2} =100$

$x^{2} =\frac{100}{3}$

$x=\sqrt{\frac{100}{3} }$

$x=\frac{\sqrt{100} }{\sqrt{3} }$

$x=\frac{10}{\sqrt{3} }$

$x=\frac{10.\sqrt{3} }{\sqrt{3}\:.\:\sqrt{3} }$

$x=\frac{10\sqrt{3} }{\sqrt{9} }$

$x=\frac{10\sqrt{3} }{3}\:m$

$V=a \times\:b\: \times\: c$

$V=x\:.\:(x-1)\:.\:(x+1)$

$V=x\:.\:(x^{2} -1)$

$V=x^{3}-x$

$V=(\frac{10\sqrt{3} }{3} )^{3} -\frac{10\sqrt{3} }{3}$

$V=\frac{10^{3}\:.\:\sqrt{3^{3} } }{3^{3} } -\frac{10\sqrt{3} }{3}$

$V=\frac{1000\:.\:\sqrt{3^{2}\:.\:3 } }{27} -\frac{10\sqrt{3} }{3}$

$V=\frac{1000\:.\:3\sqrt{3} }{27} -\frac{10\sqrt{3} }{3}$

$V=\frac{1000\sqrt{3} }{9} -\frac{10\sqrt{3} }{3}$

$V=\frac{1000\sqrt{3} }{9} -\frac{30\sqrt{3} }{9}$

$V=\frac{1000\sqrt{3}\:-\:30\sqrt{3} }{9}$

$V=\frac{(1000-30)\:.\:\sqrt{3} }{9}$

$V=\frac{970\sqrt{3} }{9}$

$V=\frac{970}{9}\:.\:\sqrt{3}$

$V=(107,77) \times\:(1,73)$

$V=186,442\:\:m^{3}$

$1m^{3}=1000\:litros$

$V=186,442\: \times1000$

$V=186.442\:litros$