c. 144π units²
Step-by-step explanation:
In the picture attached, the circle is shown.
Data
The measure of central angle QRS is: 8Ï€/9 radiansradius (r): 18 units
Area of the circle = π*r² = π*18² = 324π square units
The area of the circle is proportional to angle 2Ï€ radians. Therefore:
324Ï€ square units / shaded area = 2Ï€ radians / (8Ï€/9 radians)
shaded area = (8Ï€/9)/(2Ï€)*324Ï€
shaded area = (4/9)*324Ï€
shaded area = 144Ï€ square units