12 సెంటీమీటర్ల భుజం కలిగిన ఘనమును అన్ని ముఖాలపై ఆకుపచ్చగా రంగు వేసి, ఆపై ఒక్కొక్క భుజం 2 సెంటీమీటర్లు  ఉండే విధంగా చిన్న ఘనాలగా కత్తిరించాలి. ఒక ముఖం మాత్రమే రంగు చేయబడిన చిన్న ఘనాల సంఖ్యను కనుగొనండి.

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SSC CGL 2021 Tier-I (Held On : 18 April 2022 Shift 3)
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  1. 68
  2. 96
  3. 78
  4. 49

Answer (Detailed Solution Below)

Option 2 : 96
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12 సెంటీమీటర్ల భుజంగా కలిగిన ఘనం యొక్క అన్ని ముఖాలపై ఆకుపచ్చగా రంగు వేసి, ఆపై ఒక్కొక్క భుజం 2 సెంటీమీటర్ల చిన్న ఘనాలగా కత్తిరించాలి.

ఘనం ఇలా విభజించబడింది 12/2 = 6, అందుకే n = 6.

1 భుజం మాత్రమే రంగు వేయబడిన ఘనాల సంఖ్య

= 6(n - 2)2

= 6 (6 - 2)2

= 6 × 42

= 6 × 16

= 96

కాబట్టి, ' 96 ' సరైన సమాధానం.

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