A wire shaped into a square encloses an area of 484 square centimeters. If the same wire is reshaped into a circle, what will be the area enclosed by the circle?

Explanation

The wire's length is the perimeter of the square, which is 4 × side. Since the area of the square is 484 cm², the side length is √484 = 22 cm. Therefore, the perimeter (wire length) is 4 × 22 = 88 cm. When bent into a circle, the circumference is 88 cm. Using the formula circumference = 2πr, the radius r = 88 / (2π) = 14 / π. The area of the circle is πr² = π × (14/π)² = 196 / π ≈ 616 cm².