**Circumference** is the distance around the edge of a circle. It is similar to the perimeter of a polygon, but specifically refers to the boundary of a circle.

The formula to find the circumference of a circle is:

**C = 2πr**

Where:

- C is the circumference
- π (pi) is a constant approximately equal to 3.14159
- r is the radius of the circle

To calculate the circumference of a circle, you can use the formula C = 2πr, where r is the radius of the circle. If you are given the diameter (d) instead of the radius, you can use the formula C = πd.

The units of circumference are the same as the units of the radius. For example, if the radius is measured in meters, then the circumference will be in meters.

1. Calculate the circumference of a circle with radius 5 cm.

**Answer:** C = 2π(5) = 10π cm

2. Find the circumference of a circle with diameter 12 inches.

**Answer:** C = π(12) = 12π inches

Understanding the concept of circumference is crucial when dealing with circles. The formula C = 2πr or C = πd is used to find the circumference, and it's important to pay attention to the units of measurement.

.Study GuideMeasurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference

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 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.