Question

Find the area of a sector of the circle below. Express in terms of pie and as a decimal.

Answer 1

36π (m²) or ≈ 113.14 m²

Explanation:

`A_(circle)` =
`\pi r^(2)`

`A_(sector)` = x

`(360^o)/(40^o)` =
`(18^2 \pi )/(x)`

9 =
`(18^2 \pi )/(x)`

x = 36π

or

x ≈ 36 ×
`(22)/(7)` ≈ 113.14 m ²

Answer 2

`\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=18\\ \theta =40 \end{cases}\implies \begin{array}{llll} A=\cfrac{(40)\pi (18)^2}{360}\implies A=36\pi \\\\\\ A\approx 113.097 ~m^2 \end{array}`