Answer:
Arc length = (35pi/9) feet
Sector area = (245pi/18) feet^2
Step-by-step explanation:
We are given a circle with a central angle of 100° and a radius of 7 ft. The task at hand is that we're needing to determine the length of arc AB and the area of the shaded region.
To get arc length, we can use the formula:
Length of an Arc = [tex]\theta[/tex] × ([tex]\frac{\pi}{180}[/tex]) x r
where [tex]\theta[/tex] represents the degree, and r is the radius
Plug our values in:
Length of an Arc = 100° × [tex]\frac{\pi}{180}[/tex] × 7
Length of an Arc = [tex]\frac{35\pi}{9}[/tex]
Since the radius is units of feet, the length of the arc would be
35pi/9 feet
Now, we need to obtain the area of the shaded region, which means that we're solving for the area of a sector.
Formula for area of a sector:
[tex](\frac{\theta}{360} )[/tex] × [tex]\pi r^2[/tex]
The angle remains in degrees, and we use the same radius. So we just plug the values in again.
It becomes:
(100/360) × 49pi
= (245pi/18) ft^2
Thus the area of the shaded region is (245pi/18) ft^2.
