The ratio of the areas of two circles is 25: | vedclass

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(A) Let the radii of the two circles be $r_1$ and $r_2$ respectively.The area of a circle is given by the formula $A = \pi r^2$.The ratio of the areas

Vedclass · Accepted Answer

$5: 6$

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(A) Let the radii of the two circles be $r_1$ and $r_2$ respectively.The area of a circle is given by the formula $A = \pi r^2$.The ratio of the areas is given as $\frac{A_1}{A_2} = \frac{\pi r_1^2}{\pi r_2^2} = \frac{r_1^2}{r_2^2} = \frac{25}{36}$.Taking the square root of both sides,we get $\frac{r_1}{r_2} = \sqrt{\frac{25}{36}} = \frac{5}{6}$.The circumference of a circle is given by $C = 2\pi r$.The ratio of their circumferences is $\frac{C_1}{C_2} = \frac{2\pi r_1}{2\pi r_2} = \frac{r_1}{r_2}$.Therefore,the ratio of their circumferences is $5: 6$.

The ratio of the areas of two circles is $25: 36$. Then,the ratio of their circumferences is:

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