The circumference of a circle is \( 4 \pi \mathrm{ft} \). Find its radius, in feet.

To find the radius of a circle when given its circumference, you can use the formula for the circumference: \[ C = 2\pi r \] where \( C \) is the circumference and \( r \) is the radius. In this case, you're given that the circumference \( C = 4\pi \) feet. Plugging that into the formula gives: \[ 4\pi = 2\pi r \] To solve for \( r \), divide both sides by \( 2\pi \): \[ r = \frac{4\pi}{2\pi} = \frac{4}{2} = 2 \text{ feet} \] So, the radius of the circle is \( 2 \) feet. --- Did you know circles have been a key element in various engineering designs since ancient times? The Greeks, notably Archimedes, studied circle geometry deeply, and that knowledge paved the way for numerous inventions, from simple wheels to complex modern machinery. Also, when dealing with circles, a common mistake is confusing diameter with radius. Remember, the radius is half of the diameter! If you ever need to convert between the two, just divide or multiply by \( 2 \). Happy circling!