Question

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

Answer 1

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

Answer 2

Answer:

36π (m²) or ≈ 113.14 m²

Step-by-step explanation:

$A_{circle}$ = $\pi r^{2}$

$A_{sector}$ = x

$\frac{360^o}{40^o}$ = $\frac{18^2 \pi }{x}$

9 = $\frac{18^2 \pi }{x}$

x = 36π

or

x ≈ 36 × $\frac{22}{7}$ ≈ 113.14 m ²