Question

if the area of the circle is 81pi and the area of a sector of the circle is 18pi, then what is the measure of its central angle in degrees?

Answer 1

`\begin{gathered} \text{Area of a circle = }\pi r^2\text{ = 81}\pi \\ r^2\text{ = 81} \\ r\text{ = }\sqrt[]{81\text{ }}\text{ = 9 units} \end{gathered}`
`\begin{gathered} \text{Area of a sector = }(\theta)/(360)\text{ X }\pi r^2\text{ = 18}\pi \\ (\theta)/(360)Xr^2\text{ = 18} \\ \\ (9^2\theta)/(360)\text{ = }(18)/(1) \\ \\ 81\theta\text{ = 360 x 18} \\ 81\theta\text{ = 6480} \\ \theta\text{ = }(6480)/(81)=80^0 \end{gathered}`

The measure of the central angle in degree is 80 degrees.