Question
Download Solution PDF10 సెం.మీ వ్యాసార్థం గల ఘన గోళాన్ని సమాన వ్యాసార్థం కలిగిన 8 గోళాకార ఘన బంతులుగా కరిగించినట్లయితే, అటువంటి ప్రతి బంతి యొక్క ఉపరితల వైశాల్యం ఎంత? [π = \(\frac{{22}}{7}\) ఉపయోగించండి]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇచ్చిన:
R = 10 సెం.మీ
ఉపయోగించిన ఫార్ములా:
ఘనపరిమాణం= 4/3 x 22/7 x R x R x R
TSA(గోళం)= 4 x 22/7 x r xr
పరిష్కారం:
పెద్ద గోళం ఘనపరిమాణం= 4/3 x 22/7 x 10 3
మనకు సమాన వ్యాసార్థం కలిగిన 8 చిన్న గోళాలు ఉన్నాయి
చిన్న గోళం ఘనపరిమాణం= 4/3 x 22/7 xr 3
పెద్ద గోళం యొక్క ఘనపరిమాణం= 8 × చిన్న గోళం యొక్క ఘనపరిమాణం
4/3 x 22/7 x 103 = 8 × 4/3 x 22/7 x r3
⇒ r3 = 1000/
⇒ r = 5 సెం.మీ
TSA(గోళం)= 4 x 22/7 x 52
= 88/7 x 25
= 314.285714 = 314 \(2\over7\) cm2
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