చెక్కతో చేసిన ఒక ఘనపు దిమ్మ యొక్క కర్ణం 192 సెం.మీ. దాని ఘనపరిమాణం కనుగొనండి.

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SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 24 Jun, 2024 Shift 1)
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  1. 786432√3 cm3
  2. 766432√3 cm3
  3. 776432√3 cm3
  4. 796432√3 cm3

Answer (Detailed Solution Below)

Option 1 : 786432√3 cm3
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SSC Selection Post Phase 13 Matriculation Level (Easy to Moderate) Full Test - 01
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Detailed Solution

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ఇవ్వబడింది:

కర్ణం (d) = 192 సెం.మీ

ఉపయోగించిన సూత్రం:

d = a√3

ఇక్కడ, a = ఘనం యొక్క భుజం

ఘనపరిమాణం (V) = a3

గణనలు:

192 = a√3

⇒ a = \(\frac{192}{\sqrt{3}}\)

⇒ ఘనపరిమాణం = \(\left(\frac{192}{\sqrt{3}}\right)^3\)

⇒ ఘనపరిమాణం = \(\frac{192\times 192\times 192}{(3\sqrt{3})}\)

⇒ ఘనపరిమాణం = \(64\times 192\times 64\sqrt3\)

⇒ ఘనపరిమాణం = \(786432\sqrt3\)

∴ ఘనపు దిమ్మ యొక్క ఘనపరిమాణం \(786432\sqrt{3}\) cm3.

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