The area of a circle is \( 64 \pi \mathrm{~m}^{2} \). What is the circumference, in meters? Express y answer in terms of \( \pi \).

To find the circumference of a circle, we first need to determine its radius from the area formula \( A = \pi r^2 \). Given that \( A = 64\pi \mathrm{~m}^{2} \), we have: \[ \pi r^2 = 64\pi \] Dividing both sides by \( \pi \): \[ r^2 = 64 \] Taking the square root of both sides: \[ r = 8 \, \mathrm{m} \] Next, we use the formula for the circumference \( C = 2\pi r \): \[ C = 2\pi(8) = 16\pi \, \mathrm{m} \] So, the circumference of the circle is \( 16\pi \, \mathrm{m} \). --- Did you know that circles have fascinated mathematicians since ancient times? The ancient Greeks, notably mathematicians like Archimedes, developed many concepts related to circles, including approximations of \( \pi \) and formulas for areas and circumferences. This is why understanding circles is not just about calculations but also about appreciating their rich mathematical history! If you’re a teacher or a parent introducing circles to kids, try using real-life examples! Like measuring round objects at home—frisbees, pizzas, or even hula hoops. You can measure their diameters and calculate areas and circumferences together. It makes math fun and practical, showing how it’s all around us!