### Circumference of a Circle

#### Lesson Objective

In this lesson, we will learn about the circumference of a circle...

#### About This Lesson

In this lesson, we will:

- Learn about the formulas for the circumference of a circle.
- See an example on calculating a circle's circumference.
- See another example on finding the diameter of a circle.

The study tips and math video below will explain more.

### Study Tips

#### Tip #1

Consider a circle with the radius r. The circumference of this circle, C will be:

where π is a constant that is approximately equals to 3.14.

Now, if we have a circle with the diameter d, the formula for the circumference will be:

The math video below will give more explanation on this. Also, we will see some examples on how to use these formulas.

Circle with the radius r

Circle with the diameter d

### Math Video

#### Video on the circumference of a circle

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#### Math Video Transcript

Part 1

00:00:03.230

In this lesson, we will learn about the circumference of a circle.

00:00:09.070

Consider this circle. Now, this circle has the radius, r.

00:00:16.100

Now, the formula for the circumference of the circle, C, is given as, 2 pi r.

00:00:23.200

Alright, back to this circle.

00:00:26.230

The radius of this circle is r. Now, if we draw a line from the center, to here. We will also have the radius r.

00:00:39.030

Notice that, this is the diameter of the circle.

00:00:44.070

We can find the diameter, by adding r, with r. This gives 2r.

00:00:52.130

By letting the diameter be, 'D'. We have, 2 'R' equals to, 'D'.

00:01:00.210

Keeping this in mind, notice that, this term has '2', 'R'. By rearranging, we have pi 2 r.

00:01:11.040

Since 2'R' is equals to 'D'. This term becomes, pi 'D'.

00:01:18.230

Hence, the circumference of the circle is equals to, 2 pi r, or pi D.

00:01:26.070

That is all for this lesson. The next video will show some examples on using these formulas.

#### Examples on using the formulas: C=2πr and C=πd

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#### Math Video Transcript

Part 2

00:00:04.090

Let's take a look at some examples, on using the formula for the circumference of a circle.

00:00:10.230

In these examples, we take pi as 3.14.

00:00:16.150

Find the circumference of this circle, with the radius of 3cm.

00:00:22.190

Now, we can start with the formula for the circumference of a circle, 'C' equals to, 2 pi r.

00:00:30.210

Since the radius is given as 3cm, we can substitute 'r' with 3..

00:00:38.100

Similarly, since pi is given as 3.14, we can substitute this with, 3.14.

00:00:47.000

Now, let's calculate this.

00:00:50.140

3.14, multiply with 3, gives 9.42.

00:00:57.000

2, multiply with 9.42, gives 18.84.

00:01:03.190

Hence, we have 'C' equals to, 18.84.

00:01:09.160

Now, this number has no meaning unless we include the unit for it.

00:01:14.200

Since the radius of the circle is in centimeter, the circumference must also be in centimeter.

00:01:21.230

Hence, the circumference of the circle is, 18.84cm.

00:01:30.040

Next example. Find the diameter of this circle, when its circumference is 15.7ft.

00:01:39.080

Since we are finding the diameter, we can use the formula, 'C' equals to, pi 'D'.

00:01:47.050

We can see that, the circumference, and pi are given. Hence, we can find the diameter of the circle, by solving the equation for 'D'.

00:01:58.080

Here’s how. The circumference is given as 15.7. Hence, we can substitute 'C' with 15.7.

00:02:09.140

Next, since pi is given as 3.14. We can substitute this, with 3.14.

00:02:18.170

To find 'D', we need to remove 3.14.

00:02:24.020

We can do so, by dividing both sides of the equation with 3.14.

00:02:30.110

Hence, we get, 15.7 over 3.14 equals to 'D'.

00:02:38.120

15.7, divided by 3.14, gives 5.

00:02:44.210

Now, we have 'd', equals to 5.

00:02:49.070

Let’s rewrite this equation so that it looks neater.

00:02:54.030

Now, let’s include the unit for this number. Since the circumference is given in ft, the diameter will also be in feet.

00:03:04.010

Hence, the diameter of the circle is 5 ft.

00:03:09.170

That is all. Try out the practice question to test your understanding.

### Practice Questions & More

#### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the circumference of a circle or pick your choice of question below.

- Question 1 on finding circumference area of a circle
- Question 2 on finding the diameter of a circle

#### Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.