Answer:
[tex]\textsf{Area of a sector (angle in degrees)}=\dfrac{\theta}{360 \textdegree}\pi r^2[/tex]
[tex]\textsf{Area of a sector (angle in radians)}=\dfrac12r^2\theta[/tex]
17) Given:
- [tex]\theta[/tex] = 240°
- r = 16 ft
[tex]\textsf{Area of a sector}=\dfrac{240}{360}\pi \cdot 16^2=\dfrac{512}{3}\pi \textsf{ ft}^2[/tex]
19) Given:
- [tex]\theta=\dfrac{3 \pi}{2}[/tex]
- r = 14 cm
[tex]\textsf{Area of a sector}=\dfrac12\cdot14^2 \cdot \dfrac{3\pi}{2}=147 \pi \textsf{ cm}^2[/tex]
21) Given:
- [tex]\theta=\dfrac{ \pi}{2}[/tex]
- r = 10 mi
[tex]\textsf{Area of a sector}=\dfrac12\cdot10^2 \cdot \dfrac{\pi}{2}=25 \pi \textsf{ mi}^2[/tex]
23) Given:
- [tex]\theta[/tex] = 60°
- r = 7 km
[tex]\textsf{Area of a sector}=\dfrac{60}{360}\pi \cdot 7^2=\dfrac{49}{6}\pi \textsf{ km}^2[/tex]
