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If the ratio of the diameters of two spheres is 3 : 5, then What is the ratio of their surface areas?
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A) 9 : 25 |
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B) 9 : 10 |
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C) 3 : 5 |
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D) 27 : 125 |
Correct Answer:
| A) 9 : 25 |
Description for Correct answer:
Let the diameter's of two sphere are \( \Large d_{1} \) and \( \Large d_{2} \), respectively.
Therfore, \( \Large d_{1} : d_{2} = 3 : 5 \)
Therefore, Ratio of their surface areas = \( \Large \frac{4 \pi r_{1}^{2}}{4 \pi r_{2}^{2}} \)
= \( \Large \frac{ \left(2r_{1}\right)^{2} }{ \left(2r_{2}\right)^{2} } = \frac{d_{1}}{d_{2}} \)
= \( \Large \left(\frac{d_{1}}{d_{2}}\right)^{2} = \left(\frac{3}{5}\right)^{2} = \frac{9}{25} = 9 : 25 \)
Let the diameter's of two sphere are \( \Large d_{1} \) and \( \Large d_{2} \), respectively.
Therfore, \( \Large d_{1} : d_{2} = 3 : 5 \)
Therefore, Ratio of their surface areas = \( \Large \frac{4 \pi r_{1}^{2}}{4 \pi r_{2}^{2}} \)
= \( \Large \frac{ \left(2r_{1}\right)^{2} }{ \left(2r_{2}\right)^{2} } = \frac{d_{1}}{d_{2}} \)
= \( \Large \left(\frac{d_{1}}{d_{2}}\right)^{2} = \left(\frac{3}{5}\right)^{2} = \frac{9}{25} = 9 : 25 \)
Part of solved Volume and surface area questions and answers : >> Elementary Mathematics >> Volume and surface area
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