Question

I want to know the steps of how to get the answer to the problem as well as the actual answer

Answer 1

`\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=80\pi \end{cases}\implies 80\pi =\pi r^2 \implies \cfrac{80\pi }{\pi }=r^2 \\\\\\ 80=r^2\implies √(80)=r\\\\ -------------------------------`


`\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}\qquad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ A=36\pi\\ r=√(80) \end{cases}\implies 36\pi =\cfrac{\theta (√(80))^2}{2} \\\\\\ 72\pi =80\theta \implies \cfrac{72\pi }{80}=\theta \implies \cfrac{9\pi }{10}=\theta`


`\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=√(80)\\ \qquad √(4^2\cdot 5)\\ \qquad 4√(5)\\ \theta =(9\pi )/(10) \end{cases}\implies s=4√(5)\cdot \cfrac{9\pi }{10}\implies s=\cfrac{18\pi √(5)}{5}`