The area of the shaded sector of a circle can be calculated using the formula:
Area = (θ / 360) × π × r²
Where:
- θ = the central angle of the sector in degrees
- r = radius of the circle
To find the area, follow these steps:
- Determine the radius of the circle.
- Identify the central angle in degrees.
- Substitute the values into the formula.
- Calculate the area using the value of π (approximately 3.14159).
For example, if the radius is 5 cm and the central angle is 60 degrees, the area of the shaded sector would be:
Area = (60 / 360) × π × (5)² = (1/6) × π × 25 ≈ 13.09 cm²
This formula helps you find the area of any sector in a circle as long as you have the necessary measurements.