Basic Math 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 back0085

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