The formula to calculate the Perimeter of a Circular Segment given its central angle is:
\[ \text{Perimeter} = (\text{Radius} \times \text{Central Angle}) + (2 \times \text{Radius} \times \sin(\text{Central Angle} / 2)) \]
The Perimeter of a Circular Segment is the total length of all the boundary edges of a Circular Segment. The Radius of a Circular Segment is the radius of the circle from which the Circular Segment is cut. 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.
Let's assume the following values:
Using the formula:
\[ \text{Perimeter} = (5 \times 3.1415926535892) + (2 \times 5 \times \sin(3.1415926535892 / 2)) \approx 25.707963267946 \, \text{meters} \]
The Perimeter of the Circular Segment is approximately 25.707963267946 meters.
| Radius (meters) | Perimeter (meters) |
|---|---|
| 4 | 20.566370614356799 |
| 4.5 | 23.137166941151399 |
| 5 | 25.707963267945999 |
| 5.5 | 28.278759594740599 |
| 6 | 30.849555921535199 |