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

Answer:

Step-by-step explanation:

Let radius of small circles be r

Therefore

Circumference of small circle = 2πr

Let radius of bigger circle be R

Therefore

Circumference of bigger circle = 2πR

Given that

4x2πr=2πR

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

Now area of smaller circle =A1= 2πr^2 ...(2)

Area of bigger circle= A2 = 2πR^2

= 2π(4r)^2 (from 1)

= 2π x 16 r^2

= 16 x 2πr^2

= 16 x A1 ...(from 2)

Therefore 16A1 = A2

A2/A1 = 16 or A2:A1= 16:1

Answer 2

Answer:

area = circumference

πr^2 = 2πr

r^2 = 2r

r =2