Find the area of a sector of a circle having

Tepliwodav0 2021-11-14 Answered
Find the area of a sector of a circle having radius r and central angle \(\displaystyle\theta\). Express answers to the nearest tenth. \(\displaystyle{r}={29.2}\ {m},\ \theta={\frac{{{5}\pi}}{{{6}}}}\) radians

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Leory2000
Answered 2021-11-15 Author has 7703 answers
The area A of a sector of a circle of radius r formed by a central angle with radian measure \(\displaystyle\theta\) is
\(\displaystyle{A}={\frac{{{1}}}{{{2}}}}{r}^{{2}}\theta\)
Substitute r=29.2 m, \(\displaystyle\theta={\frac{{{5}\pi}}{{{6}}}}\) and solve for A
\(\displaystyle{A}={\frac{{{1}}}{{{2}}}}{\left({29.2}\ {m}\right)}^{{2}}\cdot{\frac{{{5}\pi}}{{{6}}}}\)
Use a calculator
\(\displaystyle{A}\approx{1116.1}\ {m}^{{2}}\)
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