Circumference of circle is 3 times circum. of a smaller circle. If the area of the larger circle is 486 in^2, what is the area of smaller circle?

Let the small circumference be C1 and the larger
circumference be C2.

Given that C2 = 3*C1
........(1)

Given the area of the larger circle is
486

==> A2 = 486

We
need to find the area of the smaller circle.

==> A2
= 486 = r2^2 * pi

==> r2^2 = 486/pi =
154.7

==> r2=
12.44

==> C2 = 2*pi*r =
78.15

But C2 = 3C1

==>
C1 = 78.15/3 = 26.05

==>  C1 = 2*pi * r1 =
26.05

==> r1 = 26.05/2pi =
4.15

==> A1 = r^2 * pi = 4.15^2 * pi =
54

Then the area of the smaller circle is 54
in^2.