Lesson 1: Perimeter and Circumference - Circumference

   Constructing Knowledge

Circumference is the special term given to the linear distance around a circle. In other words, circumference is the perimeter of a circle. In the β€œGetting Into It" activity, you discovered that the circumference of a circle (the distance around a circle) is related to the length of the diameter of the circle. If you know the diameter of a circle, you can calculate its circumference.

There are two formulas you can use to calculate the circumference of a circle.

Circumference = Ο€ Γ— diameter
= Ο€d

or

Circumference = 2 Γ— Ο€ Γ— radius
= 2Ο€r

Notice that the radius is half the diameter (or that the diameter is twice the radius)

d = 2r

   Multimedia

A video describing circumference is provided.



EXAMPLE 1

Determine the circumference of the circle.



Solution


Circumference = Ο€d
= Ο€ Γ— 18 m
= 56.5 m

The circumference of the circle is 56.5 m.

EXAMPLE 2

Determine the circumference of the circle.



Solution


C = 2Ο€r
= 2 Γ— Ο€ Γ— 45 mm
= 282.7 mm

The circumference of the circle is 282.7 mm

EXAMPLE 3

Determine the radius and diameter of a circle with a circumference of 400 m.

Solution


Step 1: Determine the diameter.

\(\begin{align} C&=\pi d \\ \\ 400\,\text{m}&=\pi d \\ \\ \frac{400\,\text{m}}{\pi}&=\frac{\cancel{\pi}d}{\cancel{\pi}} \\ \\ 127.3\,\text{m}&=d \\ \end{align}\)

The circumference is 127.3 m.

Step 2: Determine the radius, which is half of the diameter.

\(\begin{align} r&=\frac{d}{2} \\ \\ &=\frac{127.3\,\text{m}}{2} \\ \\ &=63.7\,\text{m} \\ \end{align}\)

The radius of the circle is 63.7 m.


Now, it is your turn! Complete the questions in your Chapter 7, Lesson 1 Practice Makes Perfect that refer to Circumference.



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