Basic Math 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