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vova2212 [387]
2 years ago
14

Find the surface area of a hemisphere that has a volume of 486π

title="cm^{3}" alt="cm^{3}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Xelga [282]2 years ago
6 0

\textit{volume of a hemisphere}\\ V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=486\pi \end{cases}\implies 486\pi =\cfrac{4\pi r^3}{6} \implies 6(486\pi )=4\pi r^3 \\\\\\ \cfrac{6(486\pi )}{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies \boxed{9=r} \\\\[-0.35em] ~\dotfill

\textit{surface area of a hemisphere}\\\\ SA=4\pi r^2\cdot \cfrac{1}{2}\implies \stackrel{\textit{we know that r = 9}}{SA=2\pi (9)^2}\implies SA=162\pi \implies SA\approx 508.94

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