Question

Two circles have areas in ratio 49:81 find the ratio of circumference

Answer 1

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Answer 2

Given :

Two circles have areas in ratio 49:81

To Find :

find the ratio of circumference

Solution :

Let the radius of circle 1 be r and radius of circle 2 be R

Area of circle 1 = $\pi r^2$

Area of circle 2 =$\pi R^2$

We are given that Two circles have areas in ratio 49:81

So,$\frac{ \pi r^2 }{\pi R^2}=\frac{49}{81}\\\frac{r}{R}=\sqrt{\frac{49}{81}}\\\frac{r}{R}=\frac{7}{9}$

Let the ratio be x

So, r = 7x , R= 9x

Circumference of circle 1 = $2 \pi r = 2 \pi (7x)$

Circumference of circle 2=$2 \pi r = 2 \pi (9x)$

So,the ratio of circumference=$\frac{2 \pi (7x)}{2 \pi (9x)}=\frac{7}{9}$

Hence the ratio of circumference is 7:9