Question

A sector of a circle with diameter 8 meters has an area of 22 meters squared. What is the central angle of that sector? (in degrees)

Answer 1

11π/4 radians

or 157.6 degrees

Explanation:

The sector area is a fraction of the total area of the circle; that fraction is

(central angle of sector)

------------------------------------- * circle area

2π

Here the circle area is A = π(4 m)². Inserting knowns into this formula, we get:

(central angle of sector)

------------------------------------- * π(4 m)² = 22 m²

2π

Multiplying both sides of this equation by 2π results in:

(central angle of sector) * (16 m²) = 44 m * 2π = 44π m²

Finally, we divide both sides of this equation by (16 m²):

44π m²

(central angle of sector) = ------------- = (11/4)π or 157.6 degrees

16 m²