The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is

(a) 3 : 2 (b) 4 : 9 (c) 2 : 3 (d) 81 : 16

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Solution

let radii be $r_{1}$ and $r_{2}$ ,

Ratio of areas = $\frac{π r_{1}^{2}}{π r_{2}^{2}} = \frac{9}{4}$

= $\frac{r_{1}^{2}}{r_{2}^{2}} = \frac{9}{4}$

= $\frac{r_{1}}{r_{2}} = \sqrt{\frac{9}{4}} = \frac{3}{2}$

Ratio of circumference = $\frac{2 π r_{1}}{2 π r_{2}} = \frac{r_{1}}{r_{2}} = \frac{3}{2} = 3 : 2$

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Similar questions

The circumferences of two circles are in the ratio 3 : 4. The ratio of their area is

(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

The radii of two circles are in the ratio $2 : 3$ . The ratio of their areas is
$(a)$ $2 : 3$

$(b)$ $4 : 9$

$(c)$ $3 : 2$

$(d)$ $9 : 4$

4 : 9

3 : 4

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