Question

A circle has a circumference 24.5 cm. What is the area of the circle? Use 3.14 for pie

Answer 1

`\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=24.5 \end{cases}\implies 24.5=2\pi r\implies \cfrac{24.5}{2\pi }=r\implies \implies \cfrac{12.25}{\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=(12.25)/(\pi ) \end{cases}\implies A=\pi \left( \cfrac{12.25}{\pi } \right)^2 \\\\\\ A=\cfrac{12.25^2}{\pi }\implies A=\cfrac{12.25^2}{3.14 }\implies A= 47.79`