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

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## Table of Contents

## Transcription

## Related Books

### Volume of a Rectangular Prism

#### Related Links

- Volume of a Prism = Area of the base × Height
- Volume of a Rectangular Prism = Length × Width × Height

### Volume of a Rectangular Prism

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 Rectangular Prism 0:06
- Volume of a Rectangular Prism: Formula
- Volume of a Rectangular Prism: Example
- Extra Example 1: Find the Volume of the Rectangular Prism 3:39
- Extra Example 2: Find the Volume of the Cube 5:00
- Extra Example 3: Find the Volume of the Solid 5:56

### Basic Math Online Course

### Transcription: 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 bases*0120

*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 prism*0304

*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 just*0432

*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

1 answer

Last reply by: Professor Pyo

Sat Mar 2, 2013 12:56 AM

Post by abeer aljabri on November 4, 2012

Hello,

i wanted to ask you about example 3

why you put height of prism 10 I think height is 4

V= L. W. Height

V= 4. 10. 4

I wait your answer?? thanks

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.