Answer:
Radius = 10 ft
Step-by-step explanation:
Circular Sector
The ratio between the sector's area and the circle area equals to the ratio between the sector's arc length and the circle's circumference, also equals to the ratio between the sector's angle and the circle's angle (2π or 360°).
[tex]\displaystyle\frac{sector's\ area}{circle's\ area}=\frac{sector's\ length}{circle's\ circumference}=\frac{sector's\ angle}{circle's\ angle}[/tex]
If we replace the circle's area, circumference and angle with the formula:
[tex]\boxed{\frac{sector's\ area}{\pi r^2}=\frac{sector's\ length}{2\pi r}=\frac{sector's\ angle}{2\pi\ or\ 360^o}}[/tex]
Given:
sector's area = 20π ft²
sector's angle = 72°
[tex]\displaystyle \frac{sector's\ area}{\pi r^2} =\frac{sector's\ angle}{360^o}[/tex]
[tex]\displaystyle \frac{20\pi}{\pi r^2} =\frac{72^o}{360^o}[/tex]
[tex]72\pi r^2=360(20\pi)[/tex]
[tex]r^2=100[/tex]
[tex]\bf r=10\ ft[/tex]
