Answer:
4/7 or .51 radians b) 14 square feet
Step-by-step explanation:
Radius: 7 feet
Arc length: 4 feet
Sector Area: ?
1) Since the central angle is proportional to the radius, there can be derived a formula to find it out.
L = r*α
4=7.α
4/7=7/7.α
4/7=α
2) To find the Circular Sector we need a relation between the angle, the Circle Area.
[tex]\frac{2\pi}{\alpha }=\frac{\pi r^{2}}{l} \\ \frac{2\pi}{4/7}=\frac{\pi r^{2}}{l} \\ \\2\pi l=4/7\pi r^{2} :\pi \\ 2l=4/7r^{2} \\ 2l=4/7*49\\ 2l=28\\ 2l/2=28/2\\ l=14 feet[/tex]
