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

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Related Articles:

### Prisms and Cylinders

#### Related Links

- Prism
- Polyhedron
- Three-dimensional space
- Cylinder
- Surface
- Line segment
- Volume
- Base
- Edge
- Face
- Vertex
- Solid geometry

- Prism: A polyhedron with two opposite faces that are parallel and congruent
- Polyhedrons have bases and lateral faces
- Regular prism: A prism whose faces are all the same
- Cylinders have two bases that are congruent and parallel circles
- Altitude: A segment that measures the height

### Prisms and Cylinders

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
- Prisms 0:06
- Polyhedron
- Regular Prism, Bases, and Lateral Faces
- Cylinders 9:37
- Bases and Altitude
- Extra Example 1: Classify Each Prism by the Shape of Its Bases 11:16
- Extra Example 2: Name Two Different Edges, Faces, and Vertices of the Prism 15:44
- Extra Example 3: Name the Solid of Each Object 17:58
- Extra Example 4: Write True or False for Each Statement 19:47

### Basic Math Online Course

### Transcription: Prisms and Cylinders

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over prisms and cylinders.*0002

*A prism is the first type of polyhedron or solid that we are going to go over.*0009

*Polyhedron, that sounds like a big word; but poly means many.*0017

*We are used to hearing the word polygon.*0029

*Polygon remember is like a shape where we have many sides; polygon.*0031

*Polyhedron, it is a way of saying many faces.*0038

*We are going to go over face in a bit.*0045

*But polyhedron is just when you have a three-dimensional figure, three-dimensional object.*0046

*Each side has to be straight; it has to be a segment.*0054

*That is called a polyhedron.*0062

*Another name for these three-dimensional objects are called solids.*0069

*Solids, we can have round or circular sides.*0077

*But polyhedrons, that is the only difference between them.*0084

*They are pretty much the same thing.*0086

*Solids and polyhedron, they are both talking about three-dimensional objects.*0087

*Solids, they could be circles; the sides could be circles.*0091

*For polyhedrons, each side has to be straight.*0096

*They have to be segments, line segments; many faces.*0099

*Prism is the first type.*0107

*Prism is when you have a three-dimensional object with two opposite faces that are parallel and congruent.*0110

*It is talking about faces.*0122

*Each one of these sides like this right here, this right here, and this right here, those are all faces.*0124

*All the sides of the prism, the three-dimensional solid, is a face.*0138

*When two of those faces are parallel and congruent, the two opposite faces are parallel and congruent,*0148

*then you have what is called a prism.*0158

*Those two faces that are parallel and congruent, those two are called bases.*0162

*This base, we can label as the top face and the bottom face.*0174

*You can't really see a bottom face.*0183

*Those can be labeled as bases because see how these two sides are congruent and they are parallel.*0194

*So those could be labeled as bases.*0203

*Anytime you have just two opposite faces being parallel and congruent, you have a prism.*0211

*This is called a rectangular prism because the bases are rectangles.*0217

*You are probably thinking that these two sides, the left and the right side, are also parallel and congruent.*0224

*The front and the back sides, this front and the back, are also parallel and congruent.*0231

*Rectangular prisms, you can actually label any two opposite faces as your bases.*0237

*Let me give you an example of one that is not rectangular prism.*0246

*Say I have two, three, four, five; and then I have...*0250

*When I have something like this, this is also a prism.*0266

*The bases would be this top face and this bottom face because they are both parallel and congruent.*0279

*This is called a prism; more specifically what is the base in the shape of?*0291

*What is the polygon?--this is a pentagon.*0299

*This is actually called a pentagonal prism because the base is in the shape of a pentagon; five sides.*0303

*Another example would be triangle; let's say... like that.*0313

*The bases are not going to be top and bottom.*0331

*In this case, it doesn't have to be top and bottom.*0333

*There is nowhere where it says the bases of the prism has to be top and bottom.*0335

*As long as the two faces that are opposite are both parallel and congruent.*0342

*Meaning they are facing the same direction; they are not going to ever intersect.*0351

*They are congruent; they have to be exactly the same.*0357

*This is also a prism because we do have two sides that are parallel and congruent.*0359

*This, the base is in the shape of a triangle.*0367

*This is a called a triangular prism; these are prisms.*0370

*We are pretty much only going to go over the rectangular prism.*0375

*But just so you understand what a prism is, these are just a few examples.*0379

*Again this is called base; prisms always have two bases.*0384

*We have to have two bases.*0393

*The rest of the sides, the rest of the faces, the ones that are not bases, are called lateral faces.*0396

*This right here, this right here, this side right here,*0407

*this backside right here, those are all lateral faces.*0412

*This is a lateral face, lateral face, lateral face.*0418

*This triangle is a lateral face; those are all lateral faces.*0423

*All the sides of a prism are either considered bases or lateral faces.*0428

*Regular prism; regular we know is when all the sides are the same.*0436

*It is regular; all the sides are the same; all the faces are the same.*0442

*That is what it means for a prism.*0446

*If I have a regular prism, that means all the faces are exactly the same.*0448

*They are all congruent.*0452

*If I have a rectangular prism where all the sides are the same,*0455

*then we know that each side has to be a square.*0466

*Each side of this is congruent.*0471

*This, the name for this, there is a specific name; it is a cube.*0474

*I am sure you heard of that before; cube.*0481

*A cube is a rectangular prism that is regular; regular prism.*0484

*We went over base; we went over faces; each side is a face.*0494

*This right here, each of these segments are called...*0503

*let me just draw this base to this base so you know that that is what I am talking about.*0511

*Each of these sides, these segments, they are called edges.*0517

*Edge there; this is an edge; this is an edge.*0525

*All of those are called edges; sides are faces; these are edges.*0529

*This right here is like the vertex; but the plural word for vertex is vertices.*0537

*All of these make up the vertices of a prism.*0548

*We have base or another face.*0554

*Because each one of these are faces, more specifically, this is a base.*0566

*But these are all considered faces, edges, and vertices.*0571

*The next type of solid is a cylinder; you have seen the shape before.*0579

*Maybe a can of soup; that is a cylinder.*0586

*Lot of things; a cup could be a cylinder.*0592

*A cylinder is when we have two bases that are congruent and parallel circles.*0596

*It is almost the same thing as a prism where we have two opposite faces being parallel and congruent.*0603

*With the bases, they are called bases.*0612

*But in this case, the two bases have to be circles.*0615

*If they are circles, then it is a cylinder.*0619

*We know that this is a base and this has to be the base.*0622

*Those are circles; the altitude is like the height.*0631

*A height is how tall this is; how tall is it standing; this is H.*0638

*If you lay it down sideways so it is like this, make sure that this has to be the height.*0646

*It is from base to base; that is considered the height.*0655

*Again cylinder is a solid where we have two circles as the bases and this is the height.*0661

*The altitude is the height.*0672

*Our first example is classifying each prism by the shape of its bases.*0678

*This first one, it is almost the same as the one that we went over.*0686

*The base for this, it has a few different pairs that we can label as bases.*0694

*But you can't label all of them as bases.*0702

*Only two faces can be the bases; two faces can be bases.*0704

*If you want, you can label the top and the bottom as bases.*0710

*Or if you want, you can label the front and the back.*0714

*Or the left and the right sides; as long as it is only two sides.*0716

*But make sure it is not top and like left.*0722

*They have to be opposite sides; it has to be congruent.*0725

*I want to label my top and my bottom as my bases.*0730

*Figure out this shape of the base; it is a rectangle.*0738

*It is in the shape of a rectangle; this would be a rectangular prism.*0747

*The next one, here if you look at this side right here, the left side,*0760

*left side and right side, see how they are intersecting right here.*0769

*They can't be called the bases.*0773

*Even though they are the same, they are congruent,*0774

*they are not parallel because they are intersecting.*0778

*The bottom side, this rectangle right here, is not parallel and congruent with any other side.*0782

*So it has to be this triangle here; this triangle, this front and this back.*0790

*Those would be the two bases; again parallel and congruent.*0801

*That is in the shape of a triangle; the base in the shape of a triangle.*0809

*This is called triangular prism.*0815

*Then the third one, here even though...*0826

*This one is a little bit tricky because we do have opposite sides being parallel and congruent.*0835

*But they can't be... the lateral faces... I forgot to mention this to you guys.*0840

*But lateral faces, meaning the sides that are not bases, they have to be rectangular.*0845

*This top and this bottom are the only sides that are not rectangular.*0853

*They are not rectangles; they have to be the bases.*0858

*If you are having a difficult time identifying what sides are the bases,*0870

*just look for the sides that are not rectangles.*0876

*Look for the sides that are not rectangles.*0881

*You should look at this side, the top side and the bottom side, because they are not rectangles.*0885

*Let's say those two are not parallel and congruent.*0890

*Then it wouldn't be considered a prism; it is not a prism.*0894

*This with this bottom side are the bases.*0900

*This shape, one, two, three, four, five, six.*0909

*Remember a polygon with six sides is a hexagon.*0914

*This is a hexagonal; I just put a ?al; hexagonal prism.*0919

*That is the name for this right here; they are all prisms.*0929

*This is a rectangular prism; triangular prism; hexagonal prism; based on the shape of its bases.*0935

*Next example, name two different edges, bases, and vertices of the prism.*0945

*Remember what edges are, bases are, and vertices are.*0953

*Edges are like the edges of this prism, the segments.*0958

*Two different edges; AC and DE or ED.*0966

*It doesn't matter because either way you go from here to here.*0981

*Or here to here, it is the same thing.*0984

*I can say BE; any one of these edges, you can name.*0987

*Faces... I am going to use a different color; faces.*0994

*Faces, any one of these faces; I can say CDBE; this is a rectangle.*1005

*I can say rectangle CDEB; or I can say triangle ACB.*1018

*If you recognize that this is also the base.*1039

*But remember all these sides are just called faces.*1043

*Face is another word for saying sides; face.*1046

*The last one, vertices; vertices, think of vertex, those points right there.*1053

*I can say point B; point E; those are vertices.*1065

*The third example, name the solid for each object.*1080

*We are going to see what shape, what the name of the solid is for each of these.*1086

*The first one, a can of soup.*1092

*We know a can of soup looks like this; this will be cylinder.*1094

*A shoebox, we know that a shoebox is in the shape of a prism.*1105

*More specifically, it would be a rectangular prism.*1111

*Camping tent; this one...*1116

*I am just going to draw it out for you guys so you guys can see a little bit better.*1119

*Yes, there is different versions of camping tents.*1123

*But this main one like this if you can see that... horrible at drawing... like that.*1125

*This would be... look at the bases; the bases are triangles.*1145

*This is a triangular prism.*1152

*A roll of paper towels; paper towels, it looks like this.*1161

*It has that, a little bit longer; it has the hole in the middle; like that.*1167

*This one would be cylinder.*1178

*The fourth example, we are going to write true or false for each statement.*1189

*The first one, a cylinder has congruent bases.*1193

*Cylinder, we know it must have congruent bases.*1199

*Or else it is not going to be called a cylinder.*1202

*The bases are congruent circles; so this is true.*1207

*A triangular prism has three faces; triangular prism, like this; does it have three faces?*1217

*Just the front and the back, this right here, just the bases alone, there is two.*1233

*But then you have to think that there is this side; that is three.*1242

*The other side which is this, this other side, that is four.*1248

*Then the bottom side, that is five; each one of those is faces.*1256

*Does it have three face?--no; this one is false.*1263

*A cube is a rectangular prism.*1271

*Remember a cube is a regular prism where all the sides are the same.*1275

*There is a cube; is it a rectangular prism?*1281

*Are the bases in the shape of rectangles?*1285

*It is actually in the shape of squares.*1290

*But isn't a square a type of rectangle?*1292

*So this one is true; cube is a rectangular prism.*1295

*That is it for this lesson; thank you for watching Educator.com.*1306

0 answers

Post by Bryan Watts on April 20, 2013

after about 2 years, still haven't fixed the XI to IX... ahaha

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.

1 answer

Last reply by: Mary Pyo

Sat Aug 20, 2011 12:08 AM

Post by Jasminka Usainovic on August 8, 2011

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