Circular Sector Area Calculator
This calculator helps you find the area of a circular sector, a portion of a circle defined by two radii and an arc. Ideal for geometry students and enthusiasts.
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Data Source and Methodology
All calculations are based on the standard mathematical formulas for circular sectors. For further reading, visit Wikipedia.
The Formula Explained
Area = \( \frac{1}{2} \times r^2 \times \theta \)
where \( \theta \) is in radians.
Glossary of Terms
- Radius (r): The distance from the center of the circle to any point on its circumference.
- Angle (θ): The angle subtended by the arc at the center of the circle, in degrees.
- Area: The space enclosed by the sector, measured in square units.
How It Works: A Step-by-Step Example
Consider a circle with a radius of 5 units and an angle of 60 degrees. Convert the angle to radians: \( \theta = \frac{60 \times \pi}{180} = \frac{\pi}{3} \). The area is calculated as \( \frac{1}{2} \times 5^2 \times \frac{\pi}{3} \approx 13.09 \text{ square units}\).
Frequently Asked Questions (FAQ)
What is a circular sector?
A circular sector is a portion of a circle, resembling a slice of a pie.
How do you calculate the area of a circular sector?
The area can be calculated using the formula: Area = 0.5 × r² × θ, where r is the radius and θ is the angle in radians.