Mathematics, 17.10.2019 12:30, bakerj4314
Find the surface area in terms of pie of a sphere with a volume of 72 pie cm^3
Answers: 3
![\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \begin{cases} r=radius\\ -----\\ V=72\pi \end{cases}\implies 72\pi =\cfrac{4\pi r^3}{3} \\\\\\ 216\pi =4\pi r^3\implies \cfrac{216\pi }{4\pi }=r^3\implies \sqrt[3]{54}=r\implies \boxed{3\sqrt[3]{2}=r}\\\\ -------------------------------\\\\ \textit{surface area of a sphere}\\\\ S=4\pi r^2\implies S=4\pi \left( 3\sqrt[3]{2} \right)^2\implies S=4\pi 3^2\sqrt[3]{2^2}\implies S=4\pi 9\sqrt[3]{4} \\\\\\ S=36\pi \sqrt[3]{4}](/tpl/images/0328/2949/34ab6.png)
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Find the surface area in terms of pie of a sphere with a volume of 72 pie cm^3...
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