Final answer:
The area of a sector AOB in a circle with a radius of 9 feet is 81π ft², given that sector AOB represents the entire circle. If the sector is only a fraction, the angle of the sector is needed to find the specific area of that sector.
Step-by-step explanation:
To calculate the area of sector AOB in a circle with radius 9 feet, we can use the formula for the area of a circle, A = πr². Since the radius is 9 feet, we can plug that into our formula:
A = π(9 ft)² = 81π ft².
This represents the area of the entire circle. If sector AOB represents the entire circle, then the area is 81π ft². However, if sector AOB is only a fraction of the circle, we would need to know the angle of the sector to calculate the exact area of the sector. Since the question does not specify the angle, the area of sector AOB if it is the entire circle is 81π ft², option 4).