If diagonal of the two circle is in the ratio 1:2 what will be the ratio between the area

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The areas of two circles are in the ratio 9: 4. The ratio of their circumferences isa 3: 2b 4: 9c 2: 3d 81: 16

Solution

let radii be $r_1$ and $r_2$,

Ratio of areas = $\frac{\pi r_1^2}{\pi r_2^2}=\frac{9}{4}$

= $\frac{r_1^2}{r_2^2}=\frac{9}{4}$

= $\frac{r_1}{r_2}=\sqrt{\frac{9}{4}}=\frac{3}{2}$

Ratio of circumference = $\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}=\frac{3}{2}=3:2$

Mathematics

Secondary School Mathematics X

Standard X