A) 16 : 25
B) 9 : 10
C) 3 : 5
D) 16 : 25
Correct Answer: A
Solution :
(a): Given that, let the diameters of two sphere are \[{{d}_{1}}\]and \[{{d}_{2}}\]respectively. \[\therefore {{d}_{1}}:{{d}_{2}}=4:5\] \[\therefore \]Ratio of their surface areas \[=\frac{4\pi {{r}_{1}}^{2}}{4\pi {{r}_{2}}^{2}}=\frac{{{\left( 2{{r}_{1}} \right)}^{2}}}{{{\left( 2{{r}_{2}} \right)}^{2}}}=\frac{{{d}_{1}}^{2}}{{{d}_{2}}^{2}}\] \[={{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{2}}={{\left( \frac{4}{5} \right)}^{2}}=\frac{16}{25}\] \[=16:25\]
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