How to Calculate the Circumference of a Circle

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 circumferenceC 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 traveled by Mike is

So, D = \frac{1}{2}(2 \pi r) + 2r.

Substituting, we have 514 = \pi r + 2r.

Factoring out r, we have 514 = r( \pi + 2)

514 = r(3.14 + 2)

514 = r (5.14).

Dividing both sides by 5.14, we get

r = 100.

Now, we are looking for the distance around the park (cirumfrence of the circle). That is,

C = 2 \pi r = 2 (3.14)(100)

C = 628 meters.

In the next post, we will discuss how to calculate the area of a circle.

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2 Responses

  1. July 31, 2014

    […] week, we have discussed how to calculate the circumference of a circle. In this post, we learn how to calculate the area of a circle. The area of a circle which we will […]

  2. August 6, 2014

    […] 2.) How to Calculate the Circumference of a Circle discusses how to calculate the circumference (or the distance around) of the circle. […]

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