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

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

### Volume of a Cylinder

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
- Volume of a Cylinder 0:05
- Volume of a Cylinder: Formula
- Extra Example 1: Find the Volume of the Cylinder 1:52
- Extra Example 2: Find the Volume of the Cylinder 7:38
- Extra Example 3: Find the Volume of the Cylinder 11:25

### Basic Math Online Course

### Transcription: Volume of a Cylinder

*Welcome back to Educator.com.*0001

*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 same*0029

*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 πr ^{2}; πr^{2}.*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 πr ^{2}; 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 4 ^{2}.*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 4 ^{2}; 4^{2} 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 πr ^{2} 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; 10 ^{2}, 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 πr ^{2} 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 circle*0753

*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 6 ^{2}; 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

0 answers

Post by Denise Bermudez on February 12, 2015

nevermind, sorry my mistake

0 answers

Post by Denise Bermudez on February 12, 2015

how come when you do the mathematical equation through a calculator you get 502.4 and your answer written out showing your work is 50.24?

0 answers

Post by Arpana Duggal on June 30, 2012

Hi, this section 9 is suppose to be marked IX instead of XI (11). Just letting you know.

0 answers

Post by Rishabh Kasarla on April 8, 2012

Nevermind...

sorry!

(I missed a step)

2 answers

Last reply by: Leif Djurhuus

Tue Aug 27, 2013 9:55 AM

Post by Rishabh Kasarla on April 8, 2012

For the 2nd example I thought the awnser was 251.2