Question : If the ratio of areas of two circles is 4 : 9, then the ratio of their circumferences will be:
Option 1: 3 : 2
Option 2: 9 : 4
Option 3: 2 : 3
Option 4: 4 : 9
Correct Answer: 2 : 3
Solution :
The area of the two circles is in the ratio of 4 : 9.
Let their radii be $r_1$ and $r_2$, respectively.
So, $\pi r_{1}^{2}:\pi r_{2}^{2}$ = 4 : 9
$⇒\frac{r_{1}^{2}}{r_{2}^{2}} = \frac{4}{9}$
$⇒\frac{r_{1}}{r_{2}} = \frac{2}{3}$
$\therefore$ Circumference = $2\pi r_{1}:2\pi r_{2} = \frac{2 \pi \times 2}{2 \pi \times 3}$ = 2 : 3
Hence, the correct answer is 2 : 3.
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