A circle is one of the most important shapes in mathematics. It is defined as a round shape where every point on the edge is exactly the same distance from the center. This special distance from the center to any point on the circle is called the radius.
Every circle has several important parts that we need to know. The center is the middle point of the circle. The radius is the distance from the center to any point on the edge. The diameter is the distance straight across the circle through the center. The circumference is the curved edge that goes all the way around the circle.
Now let's learn the important formulas for circles. The diameter is always twice the radius, so d equals 2r. The circumference is the distance around the circle, which equals pi times the diameter, or 2 pi r. The area inside the circle equals pi times the radius squared, written as pi r squared.
Let's work through an example problem. If a circle has a radius of 3 units, we can find all the other measurements. The diameter equals 2 times 3, which is 6 units. The circumference equals 2 pi times 3, which is 6 pi, or approximately 18.84 units. The area equals pi times 3 squared, which is 9 pi, or approximately 28.27 square units.