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Calculating the Circumference of a Circle

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Area and Circumference

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Calculating the Circumference of a Circle

Geometry

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The circumference of an object is calculated using the diameter or radius.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • After completing this Activity Object, learners will be able to:
  • Use the formula <img src../../../tutorials/images/teacherguides/US830805IE_1.png\" width=\"70\" height=\"21\" alt=\"\" border=\"0\">to calculate the circumference of a circle.
  • Use the formula <img src../../../tutorials/images/teacherguides/US830805IE_2.png\" width=\"65\" height=\"17\" alt=\"\" border=\"0\">to calculate the circumference of a circle.

Everything You'll Have Covered

The circle is the locus of all points that are at an equal distance from a given point called the center.

The basic parts of a circle are the center, diameter, radius, and circumference.

The diameter of a circle is the length of a line segment that passes through the center of circle to any point on the circle.

A 12-inch pizza is an example of a diameter: when you make the first cut to slice a round pizza pie in half, this cut is the diameter of the pizza.

Therefore, a 12-inch pizza has a 12-inch diameter.

The radius of a circle is the length of a line segment that connects the center of circle to any point on the circle.

The radius is half the length of the diameter. A circle has many different radii, each passing through the center. A real-life example of a radius is the spoke of a bicycle wheel.

The circumference of a circle is the complete distance around the outside of the circle.

The circumference of a circle can be thought of as the perimeter of the circle.

The circumference of a circle is approximately three times its diameter. If you divide the circumference by its diameter, the quotient is approximately 3.14 or pi (?). Likewise, if you tried to wrap the diameter around the circumference of the circle, you will find it takes just over three lengths of the diameter to make it all the way around the circumference. For example, the canister below has a diameter of 4.5 inches. We can determine the circumference by multiplying the diameter by pi (?).

4.5 in. 3.14 = 14.13 in.

The relationship between the diameter and circumference is explored in the activity provided in the Engaging Students section of this document. The Activity Object "Ratio of a Circle's Circumference to Its Diameter" can be used for a detailed explanation of this relationship. It is recommended that you complete "Ratio of a Circle's Circumference to Its Diameter" before using this Activity Object.

Calculating the circumference of a circle can be found using two formulas.

Depending on which information you have available, you can calculate the circumference of a circle with either:

Circumference, diameter, and radii are measured in linear units, such as inches and centimeters.

Tutorial Details

Approximate Time 15 Minutes
Pre-requisite Concepts Students should know the definitions of circle, circumference, diameter, pi, and radius.
Course Geometry
Type of Tutorial Skills Application
Key Vocabulary circle, circumference, diameter