प्लान

चाप की लंबाई और त्रिज्यखंड का क्षेत्रफल कैलकुलेटर

यह कैलकुलेटर त्रिज्या और केंद्रीय कोण से चाप की लंबाई, त्रिज्यखंड का क्षेत्रफल और जीवा की लंबाई निकालता है। कोण डिग्री या रेडियन में हो सकते हैं; डिग्री में उत्तर π के रूप में सटीक और दशमलव में भी दिए जाते हैं।

नतीजा

मान डालें और नतीजा देखने के लिए “गणना करें” दबाएँ।

सूत्र

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.

यह कैलकुलेटर कैसे इस्तेमाल करें

  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.

हल किए गए उदाहरण

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.

आम गलतियाँ

  • 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).

अक्सर पूछे जाने वाले सवाल

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.