Question
Download Solution PDFచెక్కతో చేసిన ఒక ఘనపు దిమ్మ యొక్క కర్ణం 192 సెం.మీ. దాని ఘనపరిమాణం కనుగొనండి.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇవ్వబడింది:
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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