గోళం యొక్క పరిమాణం అర్ధగోళం యొక్క పరిమాణంకు సమానం. వాటి వ్యాసార్థం యొక్క నిష్పత్తిని కనుగొనండి.

  1. 1: √3
  2. 1: √2
  3. 1: \(\sqrt[3]{4}\)
  4. 1: \(\sqrt[3]{2}\)

Answer (Detailed Solution Below)

Option 4 : 1: \(\sqrt[3]{2}\)
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PYST 1: SSC CGL - General Awareness (Held On : 20 April 2022 Shift 2)
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Detailed Solution

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ఫార్ములా:

గోళం యొక్క పరిమాణం = [4/3] × πr3

అర్ధగోళం యొక్క పరిమాణం = [2/3] × πr3

లెక్కింపు:

గోళం మరియు అర్ధగోళం యొక్క వ్యాసార్థం వరుసగా R మరియు r గా ఉండనివ్వండి

ప్రశ్న ప్రకారం

[4/3] × π × R3 = [2/3] × π × r3

⇒ R3/r3 = 1/2

⇒ R : r = 1 : ∛2

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