Question

If the circumference of One circle is 7 time of the circumference of other circle what will be ratko of the areas

Answer 1

Let the circumference of circle1 is 7 time of the circumference of circle2
circumference of circle1 = $2 \pi r_1$
circumference of circle2 = $2 \pi r_2$

Ratio = $\frac{2 \pi r_1}{2 \pi r_2} = \frac{r_1}{r_2} =7$

Area of circle1 = $\pi r_1^2$
Area of circle1 = $\pi r_2^2$

Required ratio of areas = $\frac{ \pi r_1^2}{ \pi r_2^2} = \frac{ r_1^2}{r_2^2} =( \frac{r_1}{r_2} )^2=7^2=49$

Ratio of areas is 49.

Answer 2

let radius of first circle be r and second be R
ATQ
7 2πr=2πR
7r=R
Ratio of their area=πr²/π49r²=1/49