Two circles have circumferences measuring 264 meters and 352 meters respectively. Calculate the difference in their areas between the larger and the smaller circle.

Explanation

Let the radii of the smaller and larger circles be r_s and r_l respectively. Given the circumferences, 2πr_s = 264 and 2πr_l = 352, so r_s = 264 / (2π) and r_l = 352 / (2π). The difference in areas is πr_l² - πr_s² = π(r_l² - r_s²). Substituting the values, this becomes π[(352 / 2π)² - (264 / 2π)²] = π[(176/π)² - (132/π)²] = π[(176² - 132²) / π²] = (176² - 132²) / π = (176 - 132)(176 + 132) / π = 44 × 308 / (22/7) = 44 × 308 × 7 / 22 = 4312 square meters.