The circumference of a circle is \( 7 \pi \) in. Find its radius, in inches.

To find the radius of a circle when the circumference is given, you can use the formula for circumference: \[ C = 2 \pi r \] Given that the circumference \( C = 7 \pi \), you can set up the equation: \[ 7 \pi = 2 \pi r \] Now, divide both sides by \( 2 \pi \): \[ r = \frac{7 \pi}{2 \pi} = \frac{7}{2} = 3.5 \text{ inches} \] So, the radius of the circle is \( 3.5 \) inches. Did you know that circles have intrigued humans for centuries? The ancient Greeks, particularly mathematicians like Euclid, studied their properties intensively. The pursuit of understanding circles led to advances in geometry, and the symbol for π (pi) has a rich history itself, derived from the Greek word for "perimeter." Circles aren’t just theoretical! Understanding their properties is essential in numerous fields, including engineering and architecture. For instance, when designing components like gears and wheels, knowing the radius helps ensure that parts fit together smoothly and work efficiently. This knowledge is also crucial in sports, such as calculating the size of tracks for racing or the dimensions of basketball hoops!