186k views
5 votes
If a circle with a radius of 9 and a central angle of 80° creates a shaded region… what’s the perimeter of that area

User IlDrugo
by
7.4k points

1 Answer

2 votes
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.
User Johannes Ferner
by
8.2k points

No related questions found