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### Course: Geometry (all content)>Unit 8

Lesson 1: 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
• 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.
• At , He said that it was in meters, but how could it be converted to another measurement type?
• You would just convert the dimensions. In this instance, it is 6m by 7m by 8m.

Then just do what you would regularly do when finding volume - base * height. :)
Best of luck to you!
• I'm confused, will someone explain how to do this plz?
• 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!
• help me i don't get this at all an i have a test tomorrow!
• 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.
• FOR ALL THE PEOPLE WHO DID NOT UNDERSTAND THIS VIDEO AND NEED A EASIER VERSION:
All you have to do is multiply all the sides, lets say the sides are 2in, 5in, 10in then all you have to do is 2X5X10 and thats it easy peasy
(i might be totally wrong lol pls tell me if i am)
• What would be the easier strategy to find the volume of a rectangular prism?
• 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.
• 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?
• 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.
• same thing
• How can I understand this better?
• Hi Ciamaris!

It's simple- you need to multiply the 3 dimensions- the length, height and the width!
Hope this helps!

--Strawberri
• Can I get more help on this? I'm not quite sure I understand.
• You have to multiply the width, the depth and the height to get the volume.

The volume is the space inside a 3D object. For a real life example, we can calculate the volume of a box, the measurement of a book's size, to then see how many of that same book size can fit inside a box.

In the video's case, lets look at the first example. Yellow is depth (7), height is blue (6), the base is green (8)

Volume of the box: = base x height x depth (order of multiplciation does not matter)

volume = 8 x 6 x 7
volume = 336 cubic meters