Question

The sum of circumference of four small circle of equal radius is equal to the circumference of a bigger circle. Find the ratio of the area of the bigger circle is that the smaller circle

Answer 1

Four small circles having radius$=r$

bigger circles radius is $=R.$

circumference of circle is $=2\pi r.$

$4\times 2\pi r=2\pi R$

$R=4r$

$Area=\frac{areaofbiggercircle}{areaofsmallcircle}$

$=\frac{\pi \times R\times R}{\pi \times r\times r}$

$=\frac{R^2}{r^2}=(\frac{R}{r}{)}^2$

$=4^2=16.$