Area of a Circular Sector?

A circular sector (also known as a circle sector or sector of a circle) is the portion of a circle that is enclosed between two radii and an arc. To find the area of a circular sector, we need to determine the central angle between the two radii.

Syntax

Area = ? × r² × (? / 360°)

Where:

• ? (pi) ? 3.14159
• r = radius of the circle
• ? = central angle in degrees

Example

Let's calculate the area of a circular sector with radius 5 and central angle 60° −

#include <stdio.h>

int main() {
    int radius = 5;
    int angle = 60;
    float pi = 3.14159;
    float area;
    
    /* Calculate sector area using formula: pi * r * r * (angle/360) */
    area = pi * radius * radius * angle / 360.0;
    
    printf("Radius: %d units<br>", radius);
    printf("Central angle: %d degrees<br>", angle);
    printf("Area of sector: %.2f square units<br>", area);
    
    return 0;
}

Radius: 5 units
Central angle: 60 degrees
Area of sector: 13.09 square units

Key Points

• A sector is a "slice" of a circle, like a piece of pie
• The formula works because we take a fraction (?/360°) of the total circle area (?r²)
• Always ensure the angle is in degrees when using this formula
• For angles in radians, use: Area = ½ × r² × ?

Conclusion

The area of a circular sector is calculated by taking the proportional part of the total circle area based on the central angle. This formula is essential in geometry and has practical applications in engineering and design.