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Lena [83]
3 years ago
10

Use the given circumference to find the surface area of the spherical object.

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
4 0

\bf \textit{circumference of a circle}\\\\
C=2\pi r~~
\begin{cases}
r=radius\\[-0.5em]
\hrulefill\\
C=27
\end{cases}\implies 27=2\pi r\implies \cfrac{27}{2\pi }=\boxed{r}
\\\\[-0.35em]
\rule{34em}{0.25pt}


\bf \textit{surface area of a sphere}\\\\
SA=4\pi r^2~\hspace{5em}\implies SA=4\pi \left( \boxed{\cfrac{27}{2\pi }} \right)^2\implies SA=4\pi \cdot \cfrac{27^2}{(2\pi )^2}
\\\\\\
SA=4\pi \cdot \cfrac{729}{4\pi^2}\implies SA=\cfrac{729}{\pi }\implies SA\approx 232.0479\implies SA=\stackrel{\textit{rounded up}}{232}


that is, the circumference of a circle in that sphere being 27.

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