the radius of the circle is 5 feet. It has a sector with a central angle of 54%. What is the area of the sector to the nearest tenth
+26387 the radius of the circle is 5 feet. It has a sector with a central angle of 54%.
What is the area of the sector to the nearest tenth
Central angle:
\(\begin{array}{|rcll|} \hline && 360^{\circ} \cdot 54\ \% \\ &=& 360^{\circ} \cdot \frac{54}{100} \\ &=& 3.60^{\circ} \cdot 54\\ &=& 194.4^{\circ} \\ \hline \end{array}\)
The area of the sector:
\(\begin{array}{|rcll|} \hline A_{\text{sector}} &=& \pi r^2 \cdot \frac{\varphi}{360^{\circ}} \quad & | \quad \varphi= 194.4^{\circ} \quad r = 5\ \text{feet} \\ &=& \pi \cdot 5^2 \cdot \frac{194.4^{\circ}}{360^{\circ}} \\ &=& \pi \cdot 25 \cdot 0.54 \\ &=& \pi \cdot 13.5 \\ &=& 42.4115008235 \\ \hline \end{array}\)
The area of the sector to the nearest tenth is \(42.4\ \text{feet}^2 \)
