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A sphere and a hemisphere have the same surface area. The ratio of their volumes is
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A) \( \Large \frac{\sqrt{3}}{4} : 1 \) |
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B) \( \Large 3\frac{\sqrt{3}}{4} : 1 \) |
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C) \( \Large \frac{\sqrt{3}}{8} : 1 \) |
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D) \( \Large \frac{3\sqrt{3}}{8} : 1 \) |
Correct Answer:
| D) \( \Large \frac{3\sqrt{3}}{8} : 1 \) |
Description for Correct answer:
According to the question,
Surface area of sphere = Surface area of hemisphere
\( \Large 4 \pi r_{1}^{2} = 3 \pi r_{2}^{2} = \frac{r_{1}}{r_{2}} = \frac{\sqrt{3}}{2} \)
Therefore, Ratio in volumes = \( \Large \frac{\frac{4}{3} \pi r_{1}^{3}}{\frac{4}{3} \pi r_{2}^{3}} = \frac{3\sqrt{3}}{8} : 1 \)
According to the question,
Surface area of sphere = Surface area of hemisphere
\( \Large 4 \pi r_{1}^{2} = 3 \pi r_{2}^{2} = \frac{r_{1}}{r_{2}} = \frac{\sqrt{3}}{2} \)
Therefore, Ratio in volumes = \( \Large \frac{\frac{4}{3} \pi r_{1}^{3}}{\frac{4}{3} \pi r_{2}^{3}} = \frac{3\sqrt{3}}{8} : 1 \)
Part of solved Volume and surface area questions and answers : >> Elementary Mathematics >> Volume and surface area
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