Two circles have different radii. The area of a square is 196 cm², and its side length is half the radius of the larger circle. If the radius of the smaller circle is three-sevenths of the radius of the larger circle, what is the circumference of the smaller circle?

Explanation

First, find the side length of the square: √196 = 14 cm. Since this side is half the radius of the larger circle, the radius of the larger circle is 2 × 14 = 28 cm. The radius of the smaller circle is (3/7) × 28 = 12 cm. The circumference of the smaller circle is 2π × 12 = 24π cm.