For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

## Discussion

## Study Guides

## Practice Questions

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Circumference of a Circle

#### Related Links

- Radius: A segment with one endpoint at the center and one on the circle
- Diameter: A segment that passes through the center and whose endpoints are on the circle
- Chord: A segment whose endpoints are on the circle
- Circumference: The distance around the circle
- Circumference = 2πr

### Circumference of a Circle

radius = 12 in

- C = 2πr
- C = 2(3.14)(12)
- C = 24(3.14)

radius = 5 cm

- C = 2πr
- C = 2(3.14)(5)
- C = 10(3.14)

radius = 3 in

- C = 2πr
- C = 2(3.14)(3)
- C = 6(3.14)

diameter = 8 in

- C = 2πr
- C = dπ
- C = 8(3.14)

diameter = 13 cm

- C = 2πr
- C = dπ
- C = 13(3.14)

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Circumference of a Circle

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Segments in Circles 0:05
- Radius
- Diameter
- Chord
- Circumference 2:53
- Circumference of a Circle
- Extra Example 1: Name the Given Parts of the Circle 6:26
- Extra Example 2: Find the Circumference of the Circle 7:54
- Extra Example 3: Find the Circumference of Each Circle with the Given Measure 11:04

### Basic Math Online Course

### Transcription: Circumference of a Circle

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over the circumference of a circle.*0002

*First let's go over some special segments within circles; the first is the radius.*0008

*Radius is a segment whose endpoints are on the center and on the circle.*0018

*One endpoint is on the center; the other endpoint is on the circle.*0029

*Here this segment CB or BC, doesn't matter which way, is a radius.*0034

*CA, that is also radius; I can say CA; I can say CB; I can say EC.*0043

*Those are all radius; each of those are radius; plural for radius is radii.*0056

*The next special segment is the diameter.*0071

*Diameter is a segment whose endpoints are on the circle.*0073

*It has to pass through the center.*0081

*It is like two radius put together like this back to back*0085

*to form a straight segment where each of the endpoints are on the circle.*0089

*That is a diameter; here EB, that is a diameter.*0095

*That is the only one for here.*0106

*DF, even though that segment has endpoints on the circle, it is not passing through the center.*0110

*So that is not considered a diameter.*0118

*That is actually called a chord; chord is like a diameter.*0120

*Diameter and chords, they both are similar in that they have their endpoints on the circle.*0128

*But diameter has to pass through the center; chords do not.*0134

*This is a chord; this is a diameter.*0139

*Again this is a radius; radius; this is a diameter; chord, this is a chord.*0145

*Endpoints on the circle without passing through the center, that is a chord.*0164

*The circumference is like perimeter.*0174

*We know perimeter is when you add up all the sides of some polygon.*0178

*Circumference acts as a perimeter.*0185

*But it is like the perimeter of a circle because circles, we don't have straight sides.*0187

*Instead of calling this perimeter, we call it circumference.*0196

*But it is pretty much the same thing; it is like you wrap around.*0200

*It is like if we need to build a fence around this garden.*0205

*We would call that perimeter because you are going around like this.*0214

*Let's say your garden is round like this.*0219

*Then it is not called perimeter anymore; it is called circumference.*0222

*But it is the same concept, same idea; distance around the circle.*0224

*You find that by multiplying the radius by 2 and multiplying that by π.*0230

*It is 2 times π times the radius.*0239

*When you multiply numbers together, see how we are just multiplying three numbers together.*0244

*2 and the π and the radius.*0248

*Whenever you multiply, it doesn't matter the order.*0250

*If we want, we can do 2 times π times the radius.*0253

*Or we can do radius times 2 times π or π times radius times 2.*0257

*The order doesn't matter when you multiply.*0263

*In short, this is circumference; it is 2πr; 2πr.*0270

*Since the order doesn't matter, since we are multiplying these three numbers together,*0278

*I can do 2 times r times π.*0284

*2r; if I take a radius and I multiply it by 2... that is one.*0290

*Here is another one; this is 2 times the radius.*0297

*R plus r is same thing as 2 times r; doesn't this become the diameter?*0302

*If we take 2 radius, this can also be diameter.*0308

*We can also say circumference is diameter times π; this actually has two formulas.*0315

*Circumference can be 2 times the π times the r.*0322

*Or it can be, since 2 times r equals the diameter, 2 times the radius is the diameter.*0327

*We can just say the diameter times π.*0333

*Doesn't matter which one we use; it depends on what they give us.*0341

*If we are given the radius, then we can just use 2πr.*0345

*They give us the diameter; you can just go ahead and multiply that by π.*0349

*Since you have to divide it, find the r, and then you have to multiply the 2 anyways.*0353

*If you are given radius, just use that.*0362

*If you are given diameter, just use that.*0363

*Again 2 times the π times the radius; π is 3.14; 3.14.*0366

*It is actually longer; but you only have to use 3.14.*0378

*The first example, we are going to name the given parts of the circle.*0388

*First is the chord.*0392

*Remember chord is a segment whose endpoints are on the circle.*0395

*But it doesn't pass through the center.*0400

*There is an endpoint on the circle; there is an endpoint on the circle.*0404

*A chord, you can say ED; it doesn't matter if I say DE.*0409

*Or I can say AB or BA.*0417

*The diameter, both endpoints on the circle; one, two; it passes through the center.*0422

*BE would be diameter; another one, AD is a diameter.*0434

*For radius, remember radius is endpoint on the center, endpoint on the circle.*0446

*That would be a radius; I can say CD; I can say BC.*0455

*I can say AC; I can say EC; I can say CE.*0465

*Find the circumference of the circle; this in the circle, this is the center.*0476

*This is the radius; this is the radius; it is 5.*0484

*The circumference of a circle is 2 times π times r, the radius.*0490

*It is 2 times, π is 3.14, times 5.*0500

*If you want, we can multiply this and this first.*0514

*Remember the order doesn't matter; it doesn't matter.*0517

*You can multiply this times this and then to that; it doesn't matter.*0520

*But I know that if I multiply 2 times the 5, then I get 10.*0523

*10 is an easy number to multiply with; C is 10 times 3.14.*0529

*I need to multiply these two numbers together; 3.14 times 10; 0.*0539

*1 times 4 is 4; 1 times 1 is 1; 1 times 3 is 3.*0549

*From here, since I am multiplying, how many numbers do I have behind decimal points?*0557

*I only have two.*0561

*I am going to in my answer put the decimal point in front of two numbers.*0563

*It is 31.4 or 31.40; it is the same thing.*0570

*I can just drop the 0 if I want to because it is behind the decimal point and at the end of a number.*0576

*Circumference is 31.4 or 31.40.*0584

*When I multiply by 10, there is a shortcut way of doing this.*0591

*When you multiply by 10, you see how many 0s there are.*0595

*10 has only one 0; you take the decimal point.*0600

*You are going to move it one space because there is one 0.*0605

*To determine if you are going to move it to the left or to the right,*0611

*if we are multiplying, don't we have to get a bigger number if we are multiplying by 10?*0615

*Our number has to get bigger.*0621

*If I move the decimal point to the left, my number is going to get smaller because 0.3 is not the same.*0623

*I want a bigger whole number.*0632

*I have to move it to the right to make my number bigger.*0635

*It is going to be 31.4.*0637

*Let's say I am going to multiply by 100; 100 has two 0s.*0642

*Then you would move it two spaces to the right to make it bigger.*0647

*It is going to be one, two; it is going to be 314.*0650

*That is going to be my answer; that is my circumference here.*0655

*Let's move on to the next problem.*0661

*Find the circumference of each circle with the given measure.*0666

*The first one, the radius is 9 inches.*0669

*Circumference equals 2πr, 2 times π times r.*0674

*2, π is 3.14, the radius is 9.*0684

*Again I like to multiply these two numbers first; you don't have to.*0697

*You can multiply this times this and then take that and multiply it to this again.*0701

*18; 2 times 9 is 18; times 3.14.*0707

*Now I have to multiply these two numbers; it is 3.14 times 18.*0713

*4 times 8 is 32; times 1 is 8; plus 3 is 11.*0721

*This is 24; 25; 1 times 4 is... I put a 0 up there.*0731

*1 times 4 is 4; 1 times 1 is 1; 1 times 3 is 3.*0738

*I can go ahead and add; 2 plus 0, 2.*0745

*This is 5; this is 6; this is 5.*0750

*Within my problem, how many numbers do I have behind decimal points?*0761

*I have two; from here, I am going to go one, two.*0765

*Place two numbers behind the decimal point for my answer.*0771

*My circumference becomes 56.52 inches.*0774

*It is not inches squared; only area is squared, units squared.*0789

*Circumference, you just leave it as 62.52 inches.*0794

*The next one, the diameter is 16 centimeters.*0800

*Remember if this is the formula, 2 times r becomes the diameter.*0804

*2 times radius is diameter.*0813

*I can just go ahead and say this formula is the same thing as diameter times π.*0816

*Diameter is 16; 16 times 3.14; here 3.14 times 16.*0826

*6 times 4 is 24; 6 times 1 is 6; plus 2 is 8.*0843

*6 times 3 is 18; place the 0 there; 1 times 4 is 4.*0851

*Times 1 is 1; 1 times 3 is 3; add; this is 4.*0859

*8 plus 4 is 12; 8, 9, 10; 3, 4, 5.*0865

*From here, I have two numbers total behind decimal points.*0874

*I am going to go one, two; for this one, my circumference is 50.24 centimeters.*0879

*My circumference here; and this is my circumference here.*0895

*That is it for this lesson; thank you for watching Educator.com.*0901

0 answers

Post by Victor Castillo on January 24, 2013

aaaah I see answer thanks!!!

0 answers

Post by Victor Castillo on January 24, 2013

Good question I want to know that too?

2 answers

Last reply by: Mingyang Cen

Wed Aug 15, 2018 8:16 PM

Post by javier mancha on August 23, 2011

what is pi, i understand its 3.14, i simply need to know, why is pi mentioned so much , why is pi, so important ??? I HEARD THE WORD PI a hundred times already, but no one explains , its significance