23.1 सेमी लंबाई का एक चाप, केंद्र पर 18° का कोण अंतरित करता है। वृत्त का क्षेत्रफल कितना है? [ \(π = \frac{22}{7}\) का प्रयोग कीजिए]

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SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 2)
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  1. 16978.50 सेमी2
  2. 16988.50 सेमी2
  3. 16878.50 सेमी2
  4. 16798.50 सेमी2

Answer (Detailed Solution Below)

Option 1 : 16978.50 सेमी2
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Detailed Solution

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दिया गया है:

चाप की लंबाई = 23.1 सेमी

चाप द्वारा केंद्र पर बनाया गया कोण = 18°

प्रयुक्त सूत्र:

चाप की लंबाई = (2 × π × × θ)/360

वृत्त का क्षेत्रफल = π × R2

जहाँ, R = त्रिज्या

गणना:

चाप की लंबाई = (2 × π × × θ)/360

⇒ 23.1 = (2 × 22 × R × 18)/(360 × 7)

⇒ 23.1 = (22 × R)/(10 × 7)

⇒ R = (2.1 × 70)/2 = 73.5 सेमी

वृत्त का क्षेत्रफल = π × R2

⇒ (22/7) × 73.5 × 73.5

⇒ 22 × 10.5 × 73.5

⇒ 16978.50 सेमी2

∴ सही उत्तर 16978.50 सेमी2 है।

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