Question

The ratio between the circumferences of two circles is 2:3 . Find the ratio of their areas

Answer 1

the answer is area1/area2=4/9

Answer 2

Circumference ratio 
Let the circumference of the two circles be C1 and C2 respectively.
Let the radii of the two circles be r1 and r2 respectively.
C1 : C2 = 2 : 3.
2 pi r1 : 2 pi r2
therefore,
r1 : r2 = 2 : 3

Now, the ratio of areas
= pi r1^2 : pi r2^2
= r1^2 : r2^2
= 2^2 : 3^2
= 4 : 9.