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### Course: Basic geometry and measurement > Unit 6

Lesson 2: Volume of rectangular prisms# Volume of a rectangular prism

If you want to know how much stuff you can cram into a box, finding its volume is key. To calculate the volume of a box, you need to know its height, width, and depth. You can find the volume by multiplying these three dimensions together. This formula works regardless of the units you are using (e.g. meters, feet), he method is the same - just make sure your units match up! Created by Sal Khan.

## Want to join the conversation?

- why do you multiply the lengths of the sides(37 votes)
- To calculate the area of a quadrilateral, you multiply the length times the width. An example is 5 inches into 3 inches, is 15 inches squared.(37 votes)

- At0:10, He said that it was in meters, but how could it be converted to another measurement type?(15 votes)
- You would just convert the dimensions. In this instance, it is 6m by 7m by 8m.

6m is about 19.685 feet

7m is about 22.965 feet

8m is about 26.246 feet

Then just do what you would regularly do when finding volume - base * height. :)

Best of luck to you!(26 votes)

- I'm confused, will someone explain how to do this plz?(14 votes)
- Volume is easy. For example:

Height: 5 in.

Width: 5 in.

Length: 5 in.

You can multiply length by width or width by length. If you do length by width you will get 25 and the height is 5 so multiply 25x5=125 so the volume is 125 cubic inches. Hope it helps!(8 votes)

- help me i don't get this at all an i have a test tomorrow!(11 votes)
- Volume for cubes and rectangular prisms are just

Volume = Length * Width * Height.

All you need to do now is plug the numbers in and use the right units.

If I have a box and it's 8in x 2 in x 9 in I'd do

8*2*9 = 144, but what units do I use?

My units were all in inches and because I did in*in*in my units are in^3.

It's the same for any unit of volume it's all*__*^3.(15 votes)

- What would be the easier strategy to find the volume of a rectangular prism?(6 votes)
- Good question.

The formula to solve for the volume of a rectangular prism is LxWxH.

( Length x Width x Height )

Let me demonstrate my thinking with this example.

Let's just assume that these are the numbers in the word problem, and we have to solve for V ( Volume ).

5 inches is the**Length**

8 inches is the**Width**

3 inches is the**Height**

It's pretty simple.

Just multiple all three of numbers using a calculator, or you can do it on paper, lining up all the numbers vertically.

The sum of all three numbers ( 5 x 8 x 3 ) equals 120. Therefore, the volume of the rectangular prism is 120³.**Hint**: Whenever solving for the Volume of a 3D shape, remember to cube your final answer. Like this: 120³

Hope this clears out your confusion.(11 votes)

- I'm very confused because looking back at my work, I only have
**two**identified sides (technically). I have the*width*and the*base area*which is confusing because the*base area*says that it's measured in**units squared**, so do I divide the base area by two then multiply the*width*by the*base area*by the*base area*? or no?(6 votes)- The video tells you the formula is:

Volume = Length (Width) (Height)

If you multiply any 2 of these measurements, you get the area of one side (comparable to your base). Once you multiply the the 3rd measurement, you get the volume

So, in your situation, someone as already multiplied 2 of the dimensions for you since you were given the area of the base. You just need to multiply your 2 numbers to get the volume.

Hope this helps.(7 votes)

- Can I get more help on this? I'm not quite sure I understand.(6 votes)
- Why would the first answer be 336 m3 instead of 336 m2?(2 votes)
- The first answer is 336 m3 instead of 336m2 because a rectangular prism is not flat and 2 dimensional, it is 3 dimensional it takes up space, think of it as a box. A box is not flat, rather it is three dimensional it takes up space. Compared to a flat rectangle it has volume.(4 votes)

- can you make it easy for me and other because I don't get it so make it easy for us so we can understand you. Make it easy From BLEN(2 votes)
- If a rectangular prism has a surface area of 160 units^2 and a volume of 128 units^3 and the sides are then reduced by 1/2, what is the new surface area?

I found this question on by homework and do not understand it. How would you solve it?(2 votes)

## Video transcript

What is the volume of this box? Drag on the box to rotate it. So this is pretty neat. We can actually sit
and rotate this box. And here it looks
like everything's being measured in meters. So we want to measure our
volume in terms of cubic meters. That's going to be
our unit cube here. So when we want to think about
how many cubic meters could fit in this box, we've
already seen examples. You really just have to multiply
the three different dimensions of this box. So if you wanted the
number of cubic meters that could fit in
here, it's going to be six meters times 8
meters times 7 meters which is going to give you
something in cubic meters. So let's think
about what that is. 6 times 8 is 48. Let me see if I can
do this in my head. 48 times 7, that's
40 times 7, which is going to be 280 plus
8 times 7, which is 56, 280 plus 56 is going to be 336. Let's check our answer. Let's do one more of these. So what's the
volume of this box? We'll once again, we have
its height at six feet. Now everything is
being measured in feet. We have it's width
being four feet. So we could multiple the height
times the width of four feet. And then we can multiply that
times its depth of two feet. So 6 times 4 is 24
times 2 is 48 feet. 48, and I should say cubic feet. We're saying how many
cubic feet can fit in here? When we multiply the various
dimensions measured in feet, we're counting almost
how many of those cubic feet can
fit into this box.