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# ZingPath: Circles

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## Circles

Learn in a way your textbook can't show you.
Explore the full path to learning Circles

### Lesson Focus

#### Ratio of a Circle's Circumference to Its Diameter

Pre-Algebra

You will solve problems involving the circumference of circles.

### Now You Know

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

• Explain that the constant ? is equal to the ratio of a circle’s circumference to its diameter.
• Recognize that the values 3.14 and 22/7 are often used as approximations of ?.
• Use the formula C = 2?r to solve problems.

### 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 line segment whose endpoints are on the circle and which passes through the center of 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 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.

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:

The ratio of a circle's circumference to its diameter.

The circumference of a circle is approximately three times its diameter. If you divide the circumference by its diameter, the constant ratio is called Pi, which is an irrational number shown with this symbol:

For example, the circle below has a radius of 4.5 inches.

To find the circumference:

The ratio of the circumference to its diameter can be found using the following steps:

Likewise, if you measure the diameter and circumference of the base of a soda can, you will see that the ratio of these measurements is approximately 3.14.

You can prove this relationship by finding the ratio of the circumference to diameter of any circle.

### Tutorial Details

 Approximate Time 20 Minutes Pre-requisite Concepts Learners should be familiar with circles, circumference, diameter, pi ? 3.14, and radius. Course Pre-Algebra Type of Tutorial Concept Development Key Vocabulary circle, circumference of a circle, diameter