वर्तुळाकार मैदानाभोवती वर्तुळाकार रस्ता जातो. जर जमिनीची त्रिज्या 7 मीटर असेल आणि बाह्य वर्तुळ आणि आतील वर्तुळाच्या परिघांमधील फरक 44 मीटर असेल तर रस्त्याचे क्षेत्रफळ किती आहे?

This question was previously asked in
CISF Constable/Tradesmen (2019) Official Paper (Held On : 21 March 2021)
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  1. 426 मीटर2
  2. 462 मीटर2
  3. 246 मीटर2
  4. 642 मीटर2

Answer (Detailed Solution Below)

Option 2 : 462 मीटर2
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Detailed Solution

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वापरलेले सूत्र:

वर्तुळाचे क्षेत्रफळ = π × r2

वर्तुळाचा परिघ = 2π × r

गणना:

जमिनीची त्रिज्या r आणि रस्त्याची त्रिज्या R समजू 

परिघातील फरक = 44 मीटर 

वरील सूत्र वापरून -

⇒ 2π (R - r) = 44

⇒ 2π (R - 7) = 44

(R - 7) = 44

⇒ R - 7 = 7

⇒ R = 14 मीटर 

⇒ रस्त्याचे क्षेत्रफळ = π (R2 - r2) = π (142 - 72)

⇒ रस्त्याचे क्षेत्रफळ = (22/7)× 147 = 462 मीटर2

∴ योग्य उत्तर 462 मीटर2 आहे

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