Basic Math Volume of a Rectangular Prism

Welcome back to Educator.com.0000

For the next lesson, we are going to go over the volume of a rectangular prism.0002

First let's talk about volume.0008

Volume unlike area is looking for the measurements of the space inside.0010

We talked about area and surface area.0021

Area is always just the space that it is covering.0027

But volume, it has to do with a solid, three-dimensional solid,0031

and all the space that it is covering inside.0035

If I were to take this rectangular prism, this box, and fill it with something,0037

fill it with sand or fill it with water, that would measure the volume.0043

In the volume of a prism, whether it is a rectangular prism or a triangular prism,0050

any type of prism, it is going to be this formula here: the area of the base times the height.0055

For rectangular prism, we have different pairs that we can label as the base.0064

We can label the top and the bottom as the base.0077

Remember for prisms, the base has to be parallel and congruent.0080

There is two bases.0086

It is going to be the opposite sides that are parallel and congruent.0089

Rectangular prism has a three different pairs of sides that are opposite, parallel, and congruent.0093

It is really up to you which sides you want to label as the base.0103

If I say that the top and the bottom, let's just call these the bases.0115

This top and this bottom are the bases0120

because they are opposite sides and they are parallel and congruent.0127

We are going to find the area of the base; then multiply that to the height.0132

If the area of the base is the length times the width,0141

from here, if we call this the length, we call this the width,0144

it is going to be this measure times this times the height.0149

Let's say that this right here has measures of 5; let's say this is 5.0162

The area of the base, length times the width, let's call that the area of the base.0170

That is going to be 25; let's say that the height is also 5.0174

25 times 5; that is going to be the height.0182

The volume of this is going to be 25 times 5 which is 135.0187

Once you find the volume, we know area is units squared.0195

Volume is going to be units cubed.0199

Anytime you are dealing with volume, it is always going to be units cubed.0205

If I said centimeters, 5 centimeters, then it is going to be 125 centimeters cubed.0209

Let's do a few examples; the first one, find the volume of the rectangular prism.0218

Because it is a rectangular prism, we know it is just length times the width times the height.0223

Those three measures multiply together.0229

If you want to think of it as the area of the base times the height, you can call this the base.0233

We are going to find the length times the width times the height.0243

Those three measure multiplied together is the volume.0247

Length times the width times the height.0254

We are going to say 10 meters times 4 meters times 5 meters.0261

10 times 4 is 40; 40 times 5; this 4 times 5 is 20.0274

20 and then I am going to include that 0; 40 times 5 is 200.0286

Volume is meters cubed; that is the volume of this rectangular prism.0292

Find the volume of a cube.0302

We know a cube is a special type of rectangular prism0304

and that all the sides, all the faces, are congruent.0307

All six sides are congruent.0312

Here this is 2 kilometers; this is 2 kilometers; each face is a square.0317

This is 2; then this is going to be 2.0325

We know that this is also going to be 2.0329

The volume is 2 times 2 times 2 which is...0332

2 times 2 is 4; 4 times 2 is 8.0341

The volume of this cube will be 8; we see that it is kilometers cubed.0345

For the third example, we are going to find the volume of the solid.0357

If you look here, we have two rectangular prisms and they are stacked on each other.0361

Whenever you have two different solids like this, we are going to find the volume of each one.0367

Then we can add them together.0373

It is like the volume of this bottom rectangular prism plus the volume of the top prism.0374

Let's say prism one is the one on the bottom.0383

Prism number one, volume is going to be this measure, 4 times 10.0389

Let's say that is the base.0399

I am going to color that red for the base.0402

Area of the base, 4 times 10; then times that right there.0405

4 times 10 times the other measure of 10.0414

We know 4 times 10 is 40; 40 times 10...0423

Remember whenever we multiply number to 10, we can just0432

take this number and then add this 0 to that same number.0438

40 times 10 is 400; that is meters cubed.0443

This prism here, prism number two, we can label this top one as the base.0450

The area of that... if this is 6, this side and this side are the same.0461

This side with this side are congruent.0469

If this is 6 meters, then this is also going to be 6 meters.0472

The area of the base is going to be 6 times 6.0477

The height is 2 meters; this is 36 times 2 which is 72 meters cubed.0485

I have the volume of both prisms.0505

Now I am going to add them together to find the volume of the whole solid, whole thing.0508

400 meters cubed, that is the volume of the first one.0515

Plus 72 meters cubed is going to be 472 meters cubed.0520

That is the volume of this whole thing.0531

That is it for this lesson; thank you for watching Educator.com.0536