IKI TA? Circle Sector and Segment Slices There are two main slices of a circle: The pizza slice is called a Sector. And the slice made by a chord is called a Segment. Try Them! Sector Segment Common Sectors The Quadrant and Semicircle are two special types of Sector: Half a circle is a Semicircle. Quarter of a circle is a Quadrant. Area of a Sector You can work out the Area of a Sector by comparing its angle to the angle of a full circle. Note: we are using radians for the angles. circular sector area This is the reasoning: A circle has an angle of 2π and an Area of: πr2 A Sector with an angle of θ (instead of 2π) has an Area of: (θ/2π) × πr2 Which can be simplified to: (θ/2) × r2 Area of Sector = ½ × θ × r2 (when θ is in radians) Area of Sector = ½ × (θ × π/180) × r2 (when θ is in degrees) circular sector arc length Arc Length By the same reasoning, the arc length (of a Sector or Segment) is: L = θ × r (when θ is in radians) L = (θ × π/180) × r (when θ is in degrees) Area of Segment The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here). There is a lengthy reason, but the result is a slight modification of the Sector formula: circular segment area Area of Segment = ½ × (θ - sin θ) × r2 (when θ is in radians) Area of Segment = ½ × ( (θ × π/180) - sin θ) × r2 (when θ is in degrees)
Posted on: Mon, 04 Aug 2014 12:33:25 +0000
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