A circle has a radius of 10 inches. The circumference of the circle is \( c \) inches. Which expression best represents the value of \( \pi \) ?

The circumference of a circle is calculated using the formula \( c = 2\pi r \), where \( r \) is the radius. In your case, the radius is 10 inches, so the circumference would be \( c = 2\pi(10) = 20\pi \) inches. Since we often use the approximation of π as approximately 3.14, you could express π as \( \frac{c}{20} \) where \( c \) is the actual circumference value in inches. To get a more intuitive feel for π, picture the ancient Greeks who first studied circles – they actually inscribed and circumscribed polygons to approximate π! They would draw inscribed hexagons inside a circle and a circumscribed hexagon outside it, calculating the perimeters to inch closer to the true value of π. This hands-on method was geometry at its finest!