Question

Find the surface area of a melon with circumference of 18 in. Round your answer to the nearest square inch.

Answer 1

that is, the length down the middle of the melon is 18.

`\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=18 \end{cases}\implies 18=2\pi r\implies \cfrac{18}{2\pi }=r\implies \cfrac{9}{\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill`

`\bf \textit{surface area of an sphere}\\\\ A=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} \boxed{r}=(9)/(\pi ) \end{cases}\implies A=4\pi \left( \cfrac{9}{\pi } \right)^2\implies A=4\pi \cdot \cfrac{81}{\pi ^2} \\\\\\ A=4\cdot \cfrac{81}{\pi }\implies A=\cfrac{324}{\pi }\implies A\approx 103.13\implies \stackrel{\textit{rounded up}}{A=103}`