Question

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

round your answer to the nearest whole number. C=27in. answer is 232 I'm just not sure how to work it out. Thanks!

Answer 1

`\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.