Question

the sum of circumferences of four small circles of equal radius is equal to the circumference of a bigger circle. find the ratio of the area of the bigger circle to that of the smaller circle.​

Answer 1

Ratio is

Circumference of big circle ÷ Circumference of the smaller circles

ie, 1:4

Answer 2

Hey there!

4 Circles (small) have radius = r

Circle's (big) radius = R

Circumference of circle is = 2πr

ATQ,

4 × 2πr = 2πR

R = 4r

So, R/r = 4 -----(1)

Area = area of Bigger circle/area of Small circle

= (R/r)² (R/r)²

(Using eqn. 1)

= 4 × 4 : 1

= 16 : 1

Hence,

The required ratio is 16:1

HOPE IT HELPED ^_^