Basic Math Volume of a Cylinder

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We are going to go over the volume of a cylinder.0002

Remember volume is how much space is inside the solid.0008

We are going to go over cylinder.0016

A cylinder is like a can; a can of soup; a can of corn.0017

How much space is inside?--how much can you fill it up with?0022

That is volume.0026

To find the volume of a cylinder, it is actually the same0029

exact formula as volume of rectangular prism or triangular prism.0032

Volume of a cylinder is the same as the volume of a prism.0038

We find the area of the base and multiply it to the height of the prism.0045

I am sorry... in this case, cylinder; for a cylinder, the base is a circle.0050

This up here and this down here, those are the bases.0059

For cylinder, because it is a circle, we are going to find the area of the circle.0063

Then multiply it to the height of this cylinder.0068

The area of a circle is πr²; πr².0074

That has to do with just the base; that is it.0080

Then times the height which is this right here; remember r is the radius.0083

The radius of the circle over here is from the center of the circle to a point on the circle.0090

That is radius; π is 3.14; we are going to take these measurements.0099

We are going to multiply it to find the volume of a cylinder.0109

Let's go over some examples.0112

Volume is the area of the base which is the area of a circle...0118

Let's find the area of the circle... times the height.0123

This is πr²; that is the formula to find the area of a circle.0134

Then times the height of that cylinder.0140

π is 3.14; the radius is 4; it is 4².0146

4 to the power of 2, that means 4 times 4; it is not 4 times 2.0158

The height of this cylinder from this base to the other base is 10.0164

Remember here we have to first take care of the exponent before we multiply these two numbers together.0175

Be careful not to multiply those two and then square it.0187

You will get the wrong answer.0190

This is part of order of operations when you have different things you can do.0191

We can multiply; we can take care of the exponent.0198

You always have to take care of the exponent first before you multiply.0202

If you ever see exponents, then you have to do the exponent first.0206

Then you can go ahead and multiply.0212

3.14, we are going to leave that for now.0217

Here 4²; 4² is 4 times 4; 4 times 4 is 16; then times 10.0221

Now we can go ahead and just multiply these numbers together; 3.14 times 16 times 10.0234

3.14 times 16, when you multiply numbers with decimals, you don't have to line them up.0242

That is only when you add or subtract.0255

We are just going to multiply these numbers together.0258

Ignore the decimal point for now.0260

You are just going to multiply 314 times 16.0261

4 times 6 is 24; 6 times 1 is 6; plus 2 is 8.0265

6 times 3 is 18; I am going to leave that space alone.0272

1 times 4 is 4; 1 times 1; 3.0279

Now you are going to add these number together.0285

This is 4; this is 12; this is 10; and then 5.0289

From the two original numbers, look for how many numbers are behind decimal points.0301

There is no decimal point here; you only see one.0307

I have a total of two numbers behind decimal points.0310

I am going to place two numbers behind the decimal point in my answer.0313

That is 50.24; 3.14 times 16; 50.24.0318

Then I am going to multiply this number times 10.0334

A shortcut way, remember if you are multiplying a number times 10, I have one 0 in 10.0339

I am going to take my decimal point.0349

I am just going to move it one space; one 0, one space.0351

I am going to have to move it either to the left or to the right.0359

Because I am multiplying by 10, I want to make my number bigger.0363

If I am multiplying it, then it has to get bigger.0367

In order for me to make this number... 50 is my whole number.0372

In order to make this number bigger, I need to move the decimal point over to the right.0377

It is going to now go right there.0383

My volume is... my numbers stay the same; just my decimal point moved.0386

There is the new spot for my decimal point.0393

That is going to be 50.24 times 10 again.0397

If you were to multiply this number by 100, 100 has two 0s.0404

You would move that decimal point over two spaces.0412

It would be one, two, right there.0415

Whenever you multiply a number like 10, 100, 1000, any of those numbers,0421

you are just going to count how many 0s there are in that number.0428

You are going to move your decimal point over that many spaces.0432

This right here, that is our answer; that is the volume; look for units; centimeters.0438

For volume, remember it is always going to be units cubed, to the 3rd power.0444

That is your answer, the volume for the cylinder here.0453

Let's do a couple more examples; here this circle is our base.0458

Here I have from point on the circle to another point on the circle passing through the center.0469

That is the diameter of a circle.0478

If I want to find the area of this circle here times the height, I need to find the radius.0482

I need the radius, not the diameter; it is πr² times the height.0497

Diameter is twice the length of my radius because radius goes from the center to the point on the circle.0502

That is the radius right there; from here to here, that is also radius.0510

Diameter is twice my radius.0517

To find my radius, I just have to take my diameter and divide it by 2.0523

Cut it in half; my diameter is 20; my radius will be 10.0527

It is just half the diameter; π again is 3.14; my radius is 10; squared.0536

The height of my cylinder is 8 inches.0548

Remember again be careful; do not multiply these numbers together first.0561

You have to take care of that exponent first; always exponents before multiplying.0564

Keep this number for now; 10², be careful, this is not 20.0574

It is 10 times 10 is 100; then times the 8.0578

Here we are taking a number; we are multiplying it by 100.0588

Whenever you multiply it by 100, you have two 0s there.0596

You are going to move the decimal point over two spaces.0599

Again we are going to move to the right because we want to make this number bigger.0604

If you go one, two spaces, the decimal point is going to now go behind the 4.0608

This number, after you multiply it to 100, it becomes 314.0619

Then multiply that number by our height of the cylinder which is 8.0626

314 times 8; 4 times 8 is 32; 8 times 1 is 8.0632

Add the 3; get 11; 8 times 3 is 24; plus 1 is 25.0641

I don't have any decimal points here.0649

So I don't have to move or place any decimal points in my answer.0650

The volume of this is 2512; my units, inches cubed.0655

Cubed, to the 3rd power, that is always for volume.0666

This is the volume of this cylinder.0672

Be careful if they give you the diameter; just remember radius is half the diameter.0676

You just have to divide that number by 2.0680

For the third example, here is another cylinder.0686

This cylinder is positioned a little bit differently.0691

But keep in mind, this circle is always going to be the base.0696

When we look for the area of the circle times the height,0703

the circle πr² times the height, you are always going to look for the base.0718

This right here is not the height of a cylinder.0730

Since we know that this is the base and this is the base,0734

the height is always going to be the distance between the two bases.0739

From circle to circle, that is the distance; this is actually the height.0743

Here I am given the diameter because it is from point on the circle0753

to another point on the circle passing through the center.0758

That is a diameter; I want the radius.0760

The radius is half my diameter; I just want half of that.0764

This is my radius that I want.0769

The whole thing is 12; then my radius is going to be 6.0771

π, I am going to use 3.14, the radius is 6, squared, times the height which is 7.0777

Again we have to take care of this exponent before we are going to multiply any numbers together.0792

3.14 times 6²; that is 6 times 6 which is 36.0800

Then we are going to multiply that number to 7.0811

Let's go ahead and multiply those two numbers together; 3.14 times 36.0816

4 times 6 is 24; that is 6; add the 2 is 8.0826

6 times 3 is 18; leave this space alone; 3 times 4 is 12.0833

3 times 1 is 3; add the 1 is 4; 3 times 3 is 9.0844

I am going to add these two numbers together.0853

Here is 4; that is 10; this is 9; this is 13; 9, 10, 11.0856

Now we have to go back to our original number and see how many numbers are behind decimal points.0866

Here we only have two; these two numbers are behind decimal points.0872

My answer, I am going to place two numbers behind the decimal point which is right there.0877

I get 113.04 times now this number, 7.0888

Just write it again right here; times 7.0900

4 times 7 is 28; this times this is 0; add the 2.0907

This is 21; 7; 9; and 7.0917

I have two numbers behind decimal points.0925

Then I have to place two numbers behind the decimal point here.0929

My answer then becomes... my units, centimeters to the 3rd power; units cubed.0932

That is my volume of this cylinder.0950

That is it for this lesson; thank you for watching Educator.com.0953