How to Calculate the Circumference of a Circle

July 22, 2014 Civil Service Reviewer Mathematics, Tutorials

In the previous post, we have learned about the basic terminologies about circles. We continue this series by understanding the meaning of circumference of a circle. The circumference of a circle is basically the distance around the circle itself. If you want to find the circumference of a can, for example, you can get a measuring tape and wrap around it.

The animation below shows, the meaning of circumference. As we can see, the circle with diameter 1 has circumference $\pi$ or approximately $3.14$ .

Note: If you want to know where $\pi$ came from, read Calculating the Value of Pi.

Example 1

What is the perimeter of a circle with diameter 1 unit?

Solution

The formula of finding the circumference of a circle is with circumference $C$ and diameter $d$ is $C = \pi d$ . So,

$C = \pi d = \pi(1) = \pi$ .

Example 2

Find the circumference of a circle with radius 2.5 cm.

Solution

The circumference $C$ of a circle with radius $r$ is

$C = 2 \pi r$

So, $C = 2(3.14)(2.5) = 15.7$

Therefore, the circumference of a circle with radius 2.5 cm is 15.7 cm.

Example 3

Find the radius of a circle with a circumference 18.84 cm. Use $\pi = 3.14$ .

Solution

$C = 2 \pi r$

$18.84 = 2 (3.14) r$

$18.84 = 6.28 r$

Dividing both sides by 6.28, we have

$3 = r$ .

Therefore, the radius of a circle with circumference 18.84 cm is 3 cm.

Example 4

Mike was jogging in circular park. Halfway completing the circle, he went back to where he started through a straight path. If he traveled a total distance of 514 meters, what is the total distance if he jogged around the park once? (Use $\pi = 3.14$ ).

Solution

The distance traveled by Mike is equal to half the circumference of the circular park and its diameter. Since the circumference of a circle is $2 \pi r$ and the diameter is equal to $2r$ , the distance D traveled by Mike is