To find the area of a sector, we can use the formula:
Area = (θ / 360) × π × r²
Where:
- θ is the central angle in degrees
- r is the radius of the circle
First, we need to determine the radius from the diameter. The diameter of the circle is 46 meters, so the radius (r) is:
r = diameter / 2 = 46m / 2 = 23m
Next, we can plug the values into the area formula. We have:
- θ = 210 degrees
- r = 23m
Now substituting these values in:
Area = (210 / 360) × π × (23)²
This simplifies to:
Area = (0.5833) × π × 529
Calculating the area gives:
Area ≈ 0.5833 × 3.1416 × 529 ≈ 927.18 m²
Therefore, the area of the sector with a central angle of 210 degrees and a diameter of 46m is approximately 927.18 square meters.