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A solid sphere and a solid hemisphere have the same total surface area. The ratio of their volumes is (Take, π= 22/7)
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- 3√3 : 4
- 4 : 3√3
- 3 :4√5
- 1 : 12√3
- 3√3 : 4
Correct Option: A
Radius of solid sphere = R units
Radius of solid hemisphere = r units
According to the question,
4πR² = 3πr²
⇒ 4R² = 3r²
⇒ | = | ⇒ | = | ||||
r² | 4 | r | 2 |
∴ Ratio of volumes = | πR³ | = 2 | = 2 | = | = 3√3 : 4 | ||||||||||||
3 | ³ | ³ | |||||||||||||||
πr³ | |||||||||||||||||
3 |