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?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

=> pi*(1/9)*(486/pi)

=> 486/9

=> 54 square inches

The area of the smaller circle is 54 square inches.

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