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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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- 9 : 25
- 9 : 10
- 3 : 5
- 27 : 125
Let the diameter's of two sphere are d1 and d2, respectively.
∴ Ratio of their surface areas = 4πr12/4πr22
= (2r1)2/(2r2)2 = d12/d22
= (d1/d2)2 = (3/5)2 = 9/25 = 9 : 25
Correct Answer:
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 = \( \Large \frac{4 \pi r_{1}^{2}}{4 \pi r_{2}^{2}} \)= \( \Large \frac{ \left(2r_{1}\right)^{2} }{ \left(2r_{2}\right)^{2} } = \frac{d_{1}}{d_{2}} \)
= \( \Large \left(\frac{d_{1}}{d_{2}}\right)^{2} = \left(\frac{3}{5}\right)^{2} = \frac{9}{25} = 9 : 25 \)
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