एक वृत्त के एक त्रिज्यखंड का क्षेत्रफल 66 सेमी2 है और त्रिज्यखंड का कोण 60° है। वृत्त की त्रिज्या ज्ञात कीजिए।

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SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 1)
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  1. 5 सेमी
  2. 6 सेमी
  3. 7 सेमी
  4. 3 सेमी

Answer (Detailed Solution Below)

Option 4 : 3 सेमी
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दिया गया है:

एक वृत्त के एक त्रिज्यखंड का क्षेत्रफल 66 सेमी2 है और त्रिज्यखंड का कोण 60° है।

प्रयुक्त अवधारणा:

त्रिज्यखंड का क्षेत्रफल = πr2 × θ/360°

θ = त्रिज्यखंड का कोण

r = त्रिज्या

गणना:

प्रश्न के अनुसार,

 = 66

⇒ πr2 = 66 × 6

⇒ 22/7 × r2 = 6 × 11 × 6

⇒ r2 = 126

⇒ r = 3 सेमी

इसलिए, त्रिज्या = 3 सेमी

वृत्त की त्रिज्या 3 सेमी है।

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