Ratio of circumferences of two circles = 2:3 (given)
Let the two circles be C1 and C2 with radii r1 and r2.
Circumference of circle = 2πr
Circumference of C1 = 2πr1 and
Circumference of C2 = 2πr2
(Circumference of C1) / (Circumference of C2) = (2πr1)/(2πr2)
2/3 = r1/r2
Now,
(area of C1) / (area of C2) = (πr12)/(πr22)
= {(r1)/(r2)}2
= (2/3)2
=4/9
Therefore, the required ratio is 4:9.