7.02 Circumference of a circle

The circumference of a circle is the perimeter of a circle. It can be calculated with a special formula using the radius and diameter of the circle.

The radius is the distance from the center of the circle to the circumference, and the diameter is any line that passes through the center of the circle with endpoints lying on the circumference. The diameter is equal to twice the radius.

Remember from our exploration, we have already learned about the  special value pi  , or \pi, which will help us. We found that: \pi=\dfrac{C}{d}, where C is the circumference and d is the diameter.

To find the formula for the circumference of a circle we will rearrange the ratio we used to find \pi and solve for C.

The formula for circumference of a circle is: C=\pi d and because the diameter is twice the radius, we can also write the formula as C=2\pi r.

Examples

Example 1

Find the circumference of the circle shown, correct to two decimal places.

Worked Solution

Create a strategy

The circumference of the circle can be found using the formula: C=2\pi r.

Apply the idea

\displaystyle C	\displaystyle =	\displaystyle 2\times \pi \times 6	Substitute r=6
	\displaystyle =	\displaystyle 37.70\text{ cm}	Evaluate

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Example 2

Find the circumference of the circle shown, correct to two decimal places.

Worked Solution

Create a strategy

The circumference of the circle can be found using the formula: C=\pi d.

Apply the idea

\displaystyle C	\displaystyle =	\displaystyle \pi \times 13	Substitute d=13
	\displaystyle =	\displaystyle 40.84 \text{ cm}	Evaluate

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Example 3

If the radius of a circle is equal to 17\text{ cm}, find its circumference correct to one decimal place.

Worked Solution

Create a strategy

The circumference of the circle can be found using the formula: C=2\pi r.

Apply the idea

\displaystyle C	\displaystyle =	\displaystyle 2\times \pi \times 17	Substitute r=17
	\displaystyle =	\displaystyle 106.8\text{ cm}	Evaluate

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If you take a look around, you should be able to spot some objects that have circular features. A clock face, a round plate, or the lid of a jar are some examples of things that have the outline of a circle.

For lots of other common objects there are circles present in different parts of their shape. Some examples include the rim of a cup, or the crust on a pizza.

Once we have found a feature of an object that looks like a circle, we can explore the relationship between the radius, the diameter, and the circumference of that circle. In this way we can understand more about the overall object.

We can also use these same ideas about circles to understand the circular motion of objects. Think about the way the end of the second hand moves around a clock, or the way a wheel rolls down a hill.

Examples