Mathematics, 11.03.2020 03:43 fili20
Find the radius of the sphere with a volume of 32/81π cubic yards. Write your answer as a fraction in simplest form.
The radius is
yard.
Answers: 2
![\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=\frac{32\pi }{81} \end{cases}\implies \cfrac{32\pi }{81}=\cfrac{4\pi r^3}{3}\implies \cfrac{96\pi }{81}=4\pi r^3 \\\\\\ \cfrac{96\pi }{324\pi }=r^3\implies \cfrac{8}{27}=r^3\implies \sqrt[3]{\cfrac{8}{27}}=r\implies \cfrac{\sqrt[3]{8}}{\sqrt[3]{27}}=r\implies \cfrac{2}{3}=r](/tpl/images/0542/3996/53e3b.png)
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Find the radius of the sphere with a volume of 32/81π cubic yards. Write your answer as a fraction i...
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