Pi, Circumference, and Radius

Resource for Grades 9-12

Pi, Circumference, and Radius

Media Type:
Video

Running Time: 3m 03s
Size: 1.3 MB


Resource Produced by:

KET

Collection Developed by:

KET

Collection Funded by:


A circle is a flat figure in which every point is the same distance from its center. A circle has no angles or sides, but we can still measure the distance it around it and the surface within it.

These resources are part of KET's Measurement and Geometry collection.

This video segment originally appeared in KET’s GED Connection series.

open Background Essay

A circle is a flat figure in which every point is the same distance from its center. A circle has no angles or sides, but we can still measure the distance it around it and the surface within it. Knowing the definitions of some terms will help you understand how to measure circles:

  • The circumference is the distance around the circle.
  • The radius is the distance from the center to any point on the circle.
  • The diameter is the distance across the circle through the center. The diameter is always twice the length of the radius.

In addition to definitions, there are some formulas that will help you measure a circle. For instance, if you want to know the circumference of a circle, you could wrap a string around it and then measure the string. But if you know the formula, you can determine the circumference any circle without any string at all!

The circumference of a circle is always a little larger than three times the circle’s diameter. No matter how large or small the circle, the ratio of the circumference to the diameter never changes. This ratio is named pi and is represented by the symbol π, which means “perimeter” or “periphery.”

Pi is approximately 22/7 or 3.14. You can use pi to find the approximate circumference and area of any circle. The formula for circumference is:

  • Circumference = π X diameter; π is approximately equal to 3.14.

There is also a formula for area of a circle. When finding the area of a circle, you are trying to determine the number of square units you will need to cover the surface of the circle exactly. Although square units will not fit neatly within a circular area, the following formula will help you approximate area:

  • Area = π X radius2; π is approximately equal to 3.14

open Discussion Questions

  • When would it be helpful to know the circumference and area of a circle in everyday life?
  • How does a formula help when you are trying to measure circles?

open Teaching Tips

Have learners complete the following activity from KET's Teachers' Domain

Access Sunnyside Up from this link or give learners http://goo.gl/3imXd to type into computers in the classroom. After reading the background information, ask them to click on the “chicken” tab at the top right. Read the directions, and then have learners click on the “double” tab. Watch the chart to see how the radius increases as they increase the size of the frying pan. Have learners calculate the circumference of the frying pan as the radius increases.

Using strings and rulers, have learners work in teams to measure and record the circumference of several round objects (clock, soft drink can, wastebasket, etc.) in the room. Next, ask them to measure and record each object’s diameter, and then divide its circumference by its diameter. What did they discover?


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