Calculate sector area, arc length, and perimeter from radius and central angle
Enter angle between 0 and 360 degrees
Area = (θ/360) × πr²
Where θ is the central angle in degrees and r is the radius
Example: (90/360) × π × 10² = 78.54 square units
Arc = (θ/360) × 2πr
The curved distance along the sector edge
Example: (90/360) × 2π × 10 = 15.71 units
Perimeter = 2r + Arc Length
Sum of two radii plus the arc
Example: 2(10) + 15.71 = 35.71 units
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A sector is a portion of a circle bounded by two radii and the arc between them, like a slice of pie. The sector includes the area between the two radii and the curved arc. Common examples include pizza slices, pie charts, and angular measurements in technical drawings.
The sector area formula is: Area = (θ/360) × πr², where θ is the central angle in degrees and r is the radius. For example, a sector with a 90° angle and 10 cm radius has an area of (90/360) × π × 10² = 78.54 cm². In radians, use Area = (1/2) × r² × θ.
Arc length is the distance along the curved part of the sector. Calculate it using: Arc Length = (θ/360) × 2πr, where θ is in degrees. For a 60° sector with radius 12 cm: (60/360) × 2π × 12 = 12.57 cm. In radians: Arc Length = r × θ.
The sector perimeter includes two radii plus the arc length: Perimeter = 2r + Arc Length. For example, with radius 8 cm and 45° angle: Perimeter = 2(8) + [(45/360) × 2π × 8] = 16 + 6.28 = 22.28 cm. This gives the total distance around the sector.
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