To calculate the area of a sector, we can use the formula:
- Area of a Sector = (θ / 360) × π × r²
Where:
- θ = central angle in degrees
- r = radius of the circle
In this case, we have a central angle (θ) of 210 degrees and a diameter of 46 meters. To find the radius, we will divide the diameter by 2:
- Radius (r) = Diameter / 2 = 46m / 2 = 23m
Now that we have the radius, we can plug the values into the sector area formula:
- Area = (210 / 360) × π × (23)²
Now let’s calculate:
- Area = (0.5833) × π × 529
- Area = (0.5833) × 3.14159 × 529
- Area ≈ 0.5833 × 1663.35 ≈ 968.82 m²
Thus, the area of the sector with a central angle of 210 degrees and a diameter of 46 meters is approximately 968.82 square meters.