To find the area of a sector, we can use the formula:
Area of Sector = (Central Angle / 360) × π × r²
First, we need to find the radius from the given diameter. Since the diameter is 64 meters, the radius will be:
r = Diameter / 2 = 64m / 2 = 32m
Now, we can substitute the values into the sector area formula. The central angle is given as 185 degrees:
Area of Sector = (185 / 360) × π × (32)²
Calculating the radius squared:
(32)² = 1024
Now, plugging this back into the formula:
Area of Sector = (185 / 360) × π × 1024
Using the value of π (approximately 3.14159), we can calculate:
Area of Sector ≈ (185 / 360) × 3.14159 × 1024
This will yield:
Area of Sector ≈ 0.5139 × 3.14159 × 1024 ≈ 1640.78 m²
Therefore, the area of the sector is approximately 1640.78 square meters.