Lesson 14 — Activity 3: Measuring the Circumference of Circles
Completion requirements
Lesson 14 — Activity 3:
Measuring the Circumference of
Circles
Getting Ready
Now that you have practised determining the perimeter of shapes with straight sides, you will look at finding the perimeter of circles.
The perimeter of a circle is called circumference.
You may be interested in finding the distance around many circular objects, from tires, to tablecloths, to pizzas!
This activity will show you how to measure the circumference of circles.
Think about This:
Remember that circumference is the distance around the outside surface of a circle.
Courtesy of ADLC
You will calculate the circumference of a circle by using a formula. Some formulas involve something that we call a constant. A constant never changes; it is always true.
Courtesy of Pixabay
Long ago the Ancient Greeks discovered that there was a pattern to all circles of all sizes. The distance across a circle (diameter) is related by a constant they called pi (π) to the distance around the circle (circumference). So pi is a mathematical constant that demonstrates the relationship between the diameter and circumference of a circle. The symbol for pi is π. It is pronounced "pie" and has a value of 3.14.
Watch the video below to learn more about circumference and pi.
Calculating the Circumference of a Circle
The circumference of a circle is calculated by using one of two formulas. Which one you use depends on the information that is given in the question.
C = πd OR C = 2πr
If you are given the diameter of a circle, use the formula where d is the diameter of the circle:
C = πd or C = π x diameter
Courtesy of ADLC
Courtesy of Pixabay
Let's say Danny has a bicycle tire with a diameter of 40 cm. What is the circumference? Hint: You can use the π button on your calculator!
C = πd
C = 3.14 x 40
C = 125.60
The circumference of Danny's tire is 125.60 cm.
If you are given the radius of a circle, use the formula where r is the radius of the circle:
C = 2πr or C = 2 x π x radius
C = 2πr or C = 2 x π x radius
Courtesy of ADLC
Courtesy of Pixabay
Now say Sean has a bicycle tire with a radius of 15 cm. What is the circumference?
C = 2 x π x r
C = 2 x 3.14 x 15
C = 94.2
The circumference of Sean's tire is 94.2 cm.
Try This:
Find the circumference in the following problems. You may use a calculator to solve.
Courtesy of Pixabay
1. You have a truck tire that is 42 cm in diameter. Use the correct formula from above to find the circumference of this tire.
