A circle is a closed curve in which all points on the curve are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter. The ratio of the circumference of a circle to its diameter is a constant value denoted by the Greek letter π (pi), which is approximately 3.14159. The formula for the circumference of a circle is C = 2πr, where r is the radius, and the formula for the area of a circle is A = πr^{2}.

**Radius:**The distance from the center of a circle to any point on the circle.**Diameter:**The distance across a circle passing through the center, equal to 2 times the radius.**Circumference:**The distance around the edge of a circle, given by the formula C = 2πr or C = πd, where d is the diameter.**Area:**The measure of the space enclosed by a circle, given by the formula A = πr^{2}.

**Circumference:** C = 2πr or C = πd (where r is the radius and d is the diameter)

**Area:** A = πr^{2} (where r is the radius)

- Find the circumference of a circle with a radius of 5 cm.
- Find the area of a circle with a diameter of 12 inches.

**Solution:** C = 2π(5) = 10π cm, or approximately 31.42 cm.

**Solution:** r = d/2 = 12/2 = 6 inches, A = π(6^{2}) = 36π square inches, or approximately 113.10 square inches.

In summary, a circle is a closed curve with all points equidistant from the center. The radius is the distance from the center to any point on the circle, the diameter is the distance across the circle passing through the center, the circumference is the distance around the edge of the circle, and the area is the measure of the space enclosed by the circle. Key formulas for circles include C = 2πr and A = πr^{2} for the circumference and area, respectively.

Study GuideDiameter of Circle Worksheet/Answer key

Diameter of Circle Worksheet/Answer key

Diameter of Circle Worksheet/Answer key

Diameter of Circle

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.