Question

the sum of circumference 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

let radius of smaller circles be r and that of big circle be R
acc to ques
(2pie r^2)×4=2 pir R^2
8pirr^2=2pieR^2
r^2 =R^2/4
r=R/2---------1
area of big circle /area of small circle
pieR^2/pier^2
(R/r)^2
(R/R/2)^2
4:1

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 ^_^