If the ratio of areas of two circles is 4:9, | vedclass

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Question

(A) The area of a circle is given by $A = \pi r^2$,so the area is proportional to the square of the radius $(A \propto r^2)$.Given the ratio of areas

Vedclass · Accepted Answer

$2:3$

Vedclass · Answer

(A) The area of a circle is given by $A = \pi r^2$,so the area is proportional to the square of the radius $(A \propto r^2)$.Given the ratio of areas $\frac{A_1}{A_2} = \frac{4}{9}$.Therefore,the ratio of the radii is $\frac{r_1}{r_2} = \sqrt{\frac{4}{9}} = \frac{2}{3}$.The circumference of a circle is given by $C = 2\pi r$,so the circumference is directly proportional to the radius $(C \propto r)$.Thus,the ratio of their circumferences is $\frac{C_1}{C_2} = \frac{r_1}{r_2} = \frac{2}{3}$.Hence,the ratio is $2:3$.

If the ratio of areas of two circles is $4:9,$ then the ratio of their circumferences will be

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