What is the area of the sector of a circle with θ=122°
and a diameter of 18 inches? Write your answer to two decimal places.
First, we need to find the radius of the circle, which is half of the diameter, so:
r = 18 / 2 = 9 inches
Next, we need to find the area of the entire circle:
A = πr^2
A = π(9)^2
A ≈ 254.47 square inches
Finally, we need to find the area of the sector, which is a fraction of the entire circle based on the central angle θ. Since θ=122° is less than a full circle (360°), the area of the sector will be:
Sector Area = (θ/360) * A
Sector Area = (122/360) * 254.47
Sector Area ≈ 86.37 square inches
Therefore, the area of the sector of a circle with θ=122° and a diameter of 18 inches is approximately 86.37 square inches.