Answer:
the area of the sector is 6π square inches.
Explanation:
First, we need to find the length of the arc that bounds the sector.
The circumference of the circle is 2πr, where r is the radius, so the circumference of this circle is 2π(3) = 6π inches.
To find the length of the arc that bounds the sector, we need to find what fraction of the circumference the central angle measures. The whole circle has a central angle of 360°, so if the central angle of the sector is 240°, then the fraction of the circle that it bounds is 240°/360° = 2/3.
Therefore, the length of the arc that bounds the sector is (2/3) * 6π = 4π inches.
Now, to find the area of the sector, we need to use the formula:
area of sector = (central angle / 360°) * πr^2
Plugging in the values we have:
area of sector = (240° / 360°) * π(3)^2
area of sector = (2/3) * 9π
area of sector = 6π
So the area of the sector is 6π square inches.