The formula to calculate the Area of a Circular Segment is:
\[ \text{Area} = \frac{(2 \times \text{Central Angle}) - \sin(\text{Central Angle})}{4} \times \text{Radius}^2 \]
The Area of a Circular Segment is the total quantity of plane enclosed by the boundary of a Circular Segment. The Central Angle of a Circular Segment is the angle subtended by the arc of a Circular Segment with the center of the circle from which the Circular Segment is cut. The Radius of a Circular Segment is the radius of the circle from which the Circular Segment is cut.
Let's assume the following values:
Using the formula:
\[ \text{Area} = \frac{(2 \times 3.1415926535892) - \sin(3.1415926535892)}{4} \times 5^2 \approx 39.2699081698613 \, \text{square meters} \]
The Area of the Circular Segment is approximately 39.2699081698613 square meters.
| Central Angle (radians) | Area (square meters) |
|---|---|
| 3 | 36.617999949625826 |
| 3.1 | 38.490120859791936 |
| 3.2 | 40.364838396422378 |
| 3.3 | 42.235910588395306 |
| 3.4 | 44.097131887667700 |
| 3.5 | 45.942395173060127 |
| 3.6 | 47.765752770592840 |
| 3.7 | 49.561475880678096 |
| 3.8 | 51.324111818392005 |
| 3.9 | 53.048538494899859 |