12 సెం.మీ ల వ్యాసార్థం కలిగిన ఒక గోళమును కరిగించి, 12 సెం.మీ ల ఎత్తుగల ఒక కుడి వృత్తాకార శంఖువులోకి తిరిగి వేయబడుతుంది. శంఖువు యొక్క వ్యాసార్థం కనుగొనండి :

  1. 36 సెం.మీ
  2. 32 సెం.మీ
  3. 21 సెం.మీ
  4. 24 సెం.మీ

Answer (Detailed Solution Below)

Option 4 : 24 సెం.మీ
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Detailed Solution

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ఇవ్వబడింది : 

గోళం యొక్క వ్యాసార్థం = 12 సెం.మీ 

శంఖువు యొక్క ఎత్తు = 12 సెం.మీ 

సూత్రం : 

శంఖువు యొక్క ఘనపరిమాణము = (1/3) × πr2h

గోళము యొక్క ఘనపరిమాణము = (4/3) × πr3

లెక్కింపు : 

శంఖువు యొక్క వ్యాసార్థం r గా అనుకుందాం

ఇచ్చిన ప్రశ్న ప్రకారం 

(1/3) × π × r2 × 12 = (4/3) × π × 12 × 12 × 12

⇒ r2 = 12 × 12 × 4

⇒ r = 12 × 2

∴ r = 24 సెం.మీ

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