Answer:
11π/4 radians
or 157.6 degrees
Step-by-step 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
