Question

In a circle a 60degree sector has area 25pi ft2. What is the circumference of the circle?

Answer 1

`\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta\pi r^2}{360}\implies \sqrt{\cfrac{360A}{\theta\pi }}=r\quad \begin{cases} r=radius\\ \theta=\textit{angle in degrees}\\ ----------\\ \theta=60\\ A=25\pi \end{cases} \\\\\\ \sqrt{\cfrac{360\cdot 25\pi }{60\pi }}=r\implies √(150)=r\implies 5√(6)=\boxed{r}\\\\ -----------------------------\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\implies C=2\pi \boxed{5√(6)}\implies C=10\pi √(6)`