If the ratio of the diameters of the two spheres is 3 : 5, then the ratio of their surface areas is

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1. If the ratio of the diameters of two spheres is 3: 5, then what is the ratio of their surface areas ?

1. 1. 9 : 25
   2. 9 : 10
   3. 3 : 5
   4. 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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