To find the perimeter of the shaded region in a circle with a central angle of 80° and a radius of 9, we need to determine the length of the corresponding arc.
The formula to find the length of an arc is:
Arc Length = (Central Angle / 360°) x (2πr)
where r is the radius of the circle.
In this case, the central angle is 80°, and the radius is 9. Plugging in these values into the formula, we get:
Arc Length = (80° / 360°) x (2π x 9)
Simplifying this expression:
Arc Length = (2/9) x (18π) = 4π
Therefore, the length of the shaded arc is 4π units.
To find the perimeter of the shaded region, we add the lengths of the arc and the two radii:
Perimeter = 4π + 2r = 4π + 2(9) = 4π + 18
So, the perimeter of the shaded region is 4π + 18 units.