Circumference of a Circle
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.
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 Transcript
In this lesson, we will learn about the circumference of a circle.
Consider this circle. Now, this circle has the radius, r.
Now, the formula for the circumference of the circle, C, is given as, 2 pi r.
Alright, back to this circle.
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.
Notice that, this is the diameter of the circle.
We can find the diameter, by adding r, with r. This gives 2r.
By letting the diameter be, 'D'. We have, 2 'R' equals to, 'D'.
Keeping this in mind, notice that, this term has '2', 'R'. By rearranging, we have pi 2 r.
Since 2'R' is equals to 'D'. This term becomes, pi 'D'.
Hence, the circumference of the circle is equals to, 2 pi r, or pi D.
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
Math Video Transcript
Let's take a look at some examples, on using the formula for the circumference of a circle.
In these examples, we take pi as 3.14.
Find the circumference of this circle, with the radius of 3cm.
Now, we can start with the formula for the circumference of a circle, 'C' equals to, 2 pi r.
Since the radius is given as 3cm, we can substitute 'r' with 3..
Similarly, since pi is given as 3.14, we can substitute this with, 3.14.
Now, let's calculate this.
3.14, multiply with 3, gives 9.42.
2, multiply with 9.42, gives 18.84.
Hence, we have 'C' equals to, 18.84.
Now, this number has no meaning unless we include the unit for it.
Since the radius of the circle is in centimeter, the circumference must also be in centimeter.
Hence, the circumference of the circle is, 18.84cm.
Next example. Find the diameter of this circle, when its circumference is 15.7ft.
Since we are finding the diameter, we can use the formula, 'C' equals to, pi 'D'.
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'.
Here’s how. The circumference is given as 15.7. Hence, we can substitute 'C' with 15.7.
Next, since pi is given as 3.14. We can substitute this, with 3.14.
To find 'D', we need to remove 3.14.
We can do so, by dividing both sides of the equation with 3.14.
Hence, we get, 15.7 over 3.14 equals to 'D'.
15.7, divided by 3.14, gives 5.
Now, we have 'd', equals to 5.
Let’s rewrite this equation so that it looks neater.
Now, let’s include the unit for this number. Since the circumference is given in ft, the diameter will also be in feet.
Hence, the diameter of the circle is 5 ft.
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.
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