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)

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