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Calculates the area of a circular sector (pie-slice shaped region) given radius and angle. A sector is defined by two radii and the arc between them.
Formula
A = (θ/360°) × πr² for degrees; A = ½r²θ for radians
- r
- radius (length)
- θ
- central angle (degrees or radians)
- A
- sector area (length²)
Guida passo passo
- 1Area = (θ/360) × πr² for degrees
- 2Area = ½r²θ for radians
- 3Full circle = 360° = 2π radians
- 4Half circle sector = semicircle
Esempi risolti
Ingresso
r = 8, θ = 45°
Risultato
Area = (45/360)×π×64 ≈ 25.13
Ingresso
r = 6, θ = 2 rad
Risultato
Area = ½×36×2 = 36
Domande frequenti
Can I calculate sector area if I only know the arc length?
Yes: if arc = a and radius = r, then A = ½ × r × a.
What fraction of the circle is a 60° sector?
60°/360° = 1/6 of the circle, so area = (1/6)πr².
Why are there two formulas for sector area?
One uses degrees (dividing by 360), the other uses radians (multiplying by 1/2). Use whichever unit your angle is in.
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