12 సెం.మీ వ్యాసార్ధం గల వృత్తఖండం యొక్క వైశాల్యం 32 π సెం.మీ2 వృతఖండము యొక్క సంబంధిత చాపం యొక్క పొడవును కనుగొనండి.

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SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 4)
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  1. \(\frac{16}{3}\) π సెం.మీ
  2. \(\frac{13}{3}\) π సెం.మీ
  3. \(\frac{10}{3}\) π సెం.మీ
  4. \(\frac{8}{3}\) π సెం.మీ

Answer (Detailed Solution Below)

Option 1 : \(\frac{16}{3}\) π సెం.మీ
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Detailed Solution

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ఇచ్చిన:

వృత్తఖండం వైశాల్యం = 32 π సెం.మీ2

వృత్తం యొక్క వ్యాసార్థం (R) = 12 సెం.మీ

ఉపయోగించిన ఫార్ములా:

వృత్తఖండం యొక్క వైశాల్యం= (π × R 2 × θ)/360

చాపం పొడవు = (2 × π × R × θ)/360

లెక్కింపు:

వృత్తఖండం యొక్క వైశాల్యం = (π × R 2 × θ)/360

⇒ 32π = (π × (12)2 × θ)/360

⇒ 32 × 360 = (144 × θ)

⇒ θ = (32 × 360)/144

⇒ θ = 80° 

చాపం పొడవు = (2 × π × R × θ)/360

⇒ (2 × π × 12 × 80 )/360

⇒ (16/3) × π

∴ సరైన సమాధానం \(\frac{16}{3}\) π సెం .

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