الخطط

حاسبة طول القوس ومساحة القطاع

توجد هذه الآلة الحاسبة طول القوس ومساحة القطاع وطول الوتر من نصف القطر والزاوية المركزية. يمكن أن تكون الزوايا بالدرجات أو بالراديان؛ وبالدرجات تُعطى الإجابات بدقة بدلالة π وبالأعداد العشرية أيضًا.

النتيجة

أدخل القيم واضغط احسب لرؤية النتيجة.

الصيغة

s=θ360∘×2πr=rθ (θ in radians)s = \frac{\theta}{360^\circ} \times 2\pi r = r\theta \ (\theta \text{ in radians})

The arc is the same fraction of the circumference as the angle is of a full turn.

A=θ360∘×πr2=12r2θA = \frac{\theta}{360^\circ} \times \pi r^2 = \tfrac{1}{2} r^2 \theta

The sector is the same fraction of the whole circle’s area.

c=2rsin⁡θ2c = 2r\sin\frac{\theta}{2}

The chord is the straight line joining the ends of the arc.

كيفية استخدام هذه الحاسبة

  1. Enter the radius and the central angle, and choose degrees or radians.
  2. Press Calculate to see the arc length, sector area and chord length.

أمثلة محلولة

Radius 6, angle 60°

60° is 1/6 of a full turn. Arc = 1/6 × 2π × 6 = 2π ≈ 6.283185.

Sector area = 1/6 × π × 36 = 6π ≈ 18.849556.

Chord = 2 × 6 × sin 30° = 6.

Radius 4, angle 1.5 radians

Arc = rθ = 4 × 1.5 = 6.

Area = ½ × 16 × 1.5 = 12.

Chord = 2 × 4 × sin 0.75 ≈ 5.45311.

A semicircle: radius 10, angle 180°

Arc = half the circumference = 10π.

Area = half the circle = 50π. The chord is the diameter, 20.

أخطاء شائعة

  • Using s = rθ with θ in degrees; that formula needs radians.
  • Mixing up the diameter and the radius.
  • Confusing the arc (curved) with the chord (straight).

الأسئلة الشائعة

How do you find the arc length?

Arc length = (θ/360°) × 2πr for θ in degrees, or s = rθ for θ in radians. For r = 6 and 60°: (60/360) × 12π = 2π.

How do you find the area of a sector?

Area = (θ/360°) × πr², or ½r²θ in radians. A 90° sector of radius 4 has area ¼ × 16π = 4π.

What is the difference between an arc and a chord?

The arc is the curved part of the circle between two points; the chord is the straight line joining them.