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
SiteSearch 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.