There are two circles with different radii. The radius of the smaller circle is $\frac{3}{7}$ of the radius of the larger circle. A square has an area of $3969 \text{ cm}^2$, and its side length is three times the radius of the larger circle. What is the approximate circumference of the smaller circle?

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**Solution:**

1. Calculate the side length of the square:
   - Given area of square = $3969 \text{ cm}^2$
   - Side of square = $\sqrt{3969} = 63 \text{ cm}$

2. Find the radius of the larger circle:
   - Side of square = 3 times radius of larger circle
   - So, radius of larger circle = $\frac{63}{3} = 21 \text{ cm}$

3. Calculate the radius of the smaller circle:
   - Radius of smaller circle = $\frac{3}{7} \times 21 = 9 \text{ cm}$

4. Find the circumference of the smaller circle:
   - Circumference = $2 \pi r = 2 \times \frac{22}{7} \times 9 = 56.57 \text{ cm}$
   - Approximate circumference = 56 cm

**Answer:** 56 cm

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