The radii of two spheres are in the ratio 2 : 3, then the ratio of their surface areas is ……… A) 3 : 2 B) 27 : 8 C) 8 : 27
The radii of two spheres are in the ratio 2 : 3, then the ratio of their surface areas is ………
A) 3 : 2
B) 27 : 8
C) 8 : 27
D) 4 : 9
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Correct option is: D) 4 : 9
Given that \(\frac {r_1}{r_2}\) = \(\frac 23\)
\(\therefore\) \(\frac {S_1}{S_2} = \frac {4 \pi r_1^2}{4 \pi r_2^2}\) = \((\frac {r_1}{r_2})^2 = (\frac 23)^2 = \frac 49 = 4 : 9\)
Hence, the ratio of their surface areas is 4 :9.
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