Basic Math Area of a Circle

Welcome back to Educator.com.0000

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

First to review over area, remember it is how much space it is covering up.0007

The area of a circle is when you have a circle and you see how much space it is using.0013

For example, let's say you have a hole in your jeans and you want to cover it up.0024

You cut out a circle from another pair of jeans let's say.0033

Then you stitch it on to your jeans to cover up your hole.0040

That, however much that circle, that patch is covering up, that is area.0046

It is just how much you are covering; how much space you are using.0052

Remember if you are measuring the distance around the circle, that is called circumference.0056

We have circumference which is the distance around the circle0064

and then area which is all of this, how much space it is using up.0074

The formula to find the area of a circle is π times the radius times the radius again.0083

In other words, the area is πr²; r².0090

Be careful; this is not r times 2.0097

It is an exponent; that means it is r times itself that many times.0100

It is r²; radius times the radius.0105

Circumference is 2 times π times r.0110

In this case, remember how we multiplied the 2 and the r together first.0118

In this case, this is 2 times r or r times 2.0123

This is not r times 2; this is r times r.0126

Remember keep in mind the difference between the formula for the circumference and the area.0131

First let's find the area of this circle.0139

The formula of area is π times r² or π times r times r.0143

Remember π is 3.14; π, I am going to put in 3.14.0152

The radius is 4; 4²; again be careful; this is not 4 times 2.0162

This is 4 times itself; 4 times 4.0173

Also for order of operations, because we have two different operations0182

meaning we have two different things we can do.0190

We can multiply; or we can do the exponent.0192

The order of operations, remember please excuse my dear aunt sally.0196

Parentheses, exponent, multiplication, division, addition and subtraction.0203

It is always parentheses first; exponents next; multiplication and division; addition and subtraction.0211

See how the exponent comes before multiplying.0218

Be careful; you do not multiply these two numbers first.0224

You always have to take care of the exponent first; then you can multiply.0230

3.14 times... 4² is 4 times 4 which is 16.0240

Again remember do not multiply 3.14 times 4 and then square it.0249

If you do that, you are going to get the wrong answer.0254

Here I want to multiply 3.14 times 16.0257

4 times 6 is 24; 6 times 1 is 6; plus 2 is 8.0266

6 times 3 is 18; I put a 0 right here.0272

1 times 4, 4; 1 times 1, 1; 1 times 3, 3; then add.0279

4 plus 0 is 4; this is 12; 8, 9, 10; 3, 4, 5.0290

Since I am multiplying, I look at my problem.0303

I see how many numbers are behind the decimal point.0307

I only have two numbers behind decimal points.0310

In my answer, I am going to place two numbers behind the decimal point which is right there.0314

My answer becomes 50.24; I cannot forget my units; here it is inches.0319

Area is always squared; units squared; not numbers squared; units squared.0333

50.24 inches squared is my answer; that is the area of this circle.0339

Next example, here I am given that the diameter...0348

Remember diameter is a segment whose endpoints are on the circle; on the circle; on the circle.0356

And passes through the middle, the center of the circle.0364

This is a diameter; the diameter is 20 meters.0368

To find the area of a circle, area equals πr², radius squared.0374

I need to find the radius; I have the diameter; but I want the radius.0382

How do I find the radius if I am given the diameter?0390

The whole thing is 20; that is the diameter.0393

I know the radius is from the center to this point right there.0395

The radius is half the diameter.0401

If the whole thing is 20, then the radius has to be half of that which is 10.0403

Now I know my radius is 10.0413

I can go ahead and plug in my numbers and solve for my area.0415

π is 3.14; the radius is 10².0420

Again order of operations says we have to take care of the exponents before multiplying.0428

Area equals... I am going to leave this for the next step.0437

10² is not 10 times 2; it is not 20; be careful.0442

It is 10 times 10 which is 100; remember the shortcut.0446

If we want to multiply by 10 or 100 or 1000 or 10000,0457

then you just count the number of 0s in that number.0464

Here I have two 0s; 100 has two 0s.0467

You are going to take this decimal point then.0473

Whenever you multiply a number to 100 or 10 or 1000, count how many 0s there are.0477

There is two; I am going to place this decimal point.0483

I am going to move it two spaces then.0488

Two 0s so I am going to move it two spaces.0490

Do I move it to the left or to the right two spaces?0493

Since I am multiplying by 100, this number has to get bigger.0500

The way to make the number bigger is to move the decimal point over to the right0504

because you want the whole number to be a bigger whole number.0508

I have to move it to the right two spaces; go one, two.0512

My answer then becomes... that is the new spot for my decimal point.0516

It is 314 is my answer; 314.0522

Again two 0s here; move it two spaces to the right.0529

It was here; it moved over to here, the end.0534

Since it is at the end, I don't have to write it.0537

It is just 314 point... same thing as if not being there.0539

314, you can leave it like that.0545

We are done solving; but I have to add my units now.0550

It is meters; area is always squared; units squared; 314 meters squared.0552

My third example, we are going to find the area of the shaded region.0564

I have this rectangle and a circle here that is cut out.0572

All this is missing; that is area.0582

If I cut it out, then don't I have to take it away?0587

I have to subtract it; it is as if I have this whole rectangle.0591

It was whole before the circle was cut out.0599

Find the area of the whole thing.0602

Then you are going to subtract the area of the circle.0605

That is going to become what you have left, the area that is shaded.0609

Imagine if this rectangle was like a piece of paper and you cut out a circle.0617

You have to figure out what is that area of the circle you cut out to see what you are taking away.0625

Find the area of rectangle; find the area of the circle; subtract it.0632

You will get the area of the shaded region.0637

The area of the rectangle; this is the rectangle.0640

Area is base times height or length times width; length times the width.0645

That is 8 times 7 which is 56 centimeters squared.0659

Centimeters squared is the area of this rectangle; that is that.0674

The area of the circle, πr²; π is 3.14; the radius is 2; 2².0683

I am going to take care of this first.0705

Area equals 3.14... I am going to leave that; solve that out; that is 4.0707

3.14 times the 4; let's do that over here; 3.14 times 4.0716

4 times 4 is 16; 4 times 1 is 4; plus 1 is 5.0723

This is 12; I have two numbers behind the decimal point; one, two.0730

I need to place two numbers behind the decimal point in my answer.0737

Area equals 12.56 centimeters squared.0742

Now I have the area of the whole thing and then the area of the circle.0752

I need to take away the circle from the rectangle.0755

It is going to be 56 minus 12.56; I need to do that.0760

56 minus... remember when you subtract decimals, you have to line them up.0774

Where is the decimal in this number?0782

If you don't see it, it is always at the end right there.0784

Minus 12 point... make sure only when you add or subtract, the decimals have to line up... 56.0788

I am missing numbers here.0800

If I am missing numbers here, it is at the end of a number behind the decimal point, I can add 0s like that.0802

When I subtract, this is going to borrow; this becomes the 10; this becomes 9.0811

Borrow; 5; is that big enough?--yes.0821

10 minus this 6 is 4; 9 minus 5 is 4; point.0827

5 minus 2 is 3; 5 minus 1 is 4; it is 43.44.0837

This is 43.44 centimeters squared is my answer.0849

Again just find the area of the rectangle; then find the area of the circle.0860

I subtract it; I have to take the circle away; I have to subtract it.0866

Make sure your decimals line up when you subtract; you get this as your answer.0872

That is it for this lesson; thank you for watching Educator.com.0881