Question : The ratio of areas of two circles is 81 : 121. What will be the ratio of their circumferences?
Option 1: 9 : 11
Option 2: 121 : 81
Option 3: 11 : 9
Option 4: 81 : 121
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Correct Answer: 9 : 11
Solution : Given, ${{A{_1}}}:{A{_2}}=81:121$ Area $\propto$ circumference$^2$ ⇒ $\frac{C{_1}}{C{_2}}=\frac{\sqrt{A{_1}}}{\sqrt {A{_2}}}$, where $C{_1}\text{ and }C{_2}$ are the circumference, and $A{_1}\text{ and }A{_2}$ are the area. ⇒ $\frac{C{_1}}{C{_2}}=\frac{\sqrt{81}}{\sqrt{121}}$ ⇒ $\frac{C{_1}}{C{_2}}=\frac{9}{11}$ Hence, the correct answer is 9 : 11.
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