Question

the sum of circumference of four small circle of equal radius is equal to the circumference of bigger circle find the ratio of the area of the bigger Circle to that of the smaller circle​

Answer 1

Step-by-step explanation:

Given that:-

2πr+2πr+2πr+2πr = 2πR

2π(r+r+r+r) = 2πR

4r = R............(1)

Area of bigger circle= πR^2

So, from (1)= π(4r)^2

= π16r^2

Area of smaller circle= πr^2

Ratio of area of bigger circle to smaller circle. = π16r^2/πr^2

= 16/1

Hence,

Ratio of area of bigger circle to smaller circle. =16:1

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 ^_^