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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.
The circumference of the circle is 3 times that of a smaller circle. The circumference of a circle is given by 2*pi*r, where r is the radius. The are of a circle is given by pi*r^2 where r is the radius. The area of the larger circle is 486.
The radius of the larger circle is sqrt (486/pi).
The area of the smaller circle is pi*[(1/3)*sqrt (486/pi)]^2
=> 54 square inches
The area of the smaller circle is 54 square inches.
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