+0

# 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

0
213
2

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

Guest Apr 6, 2017
Sort:

#1
+18827
+3

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 $$42.4\ \text{feet}^2$$

heureka  Apr 6, 2017
#2
0

The answer is 24 inches or cm

Guest Apr 6, 2017

### 23 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details