Main content

### Course: 6th grade foundations (Eureka Math/EngageNY) > Unit 5

Lesson 4: Topic D: Foundations# Volume through decomposition

Explore the concept of finding the volume of complex shapes by decomposing them into simpler, non-overlapping rectangular prisms. Understand the additive nature of volume and demonstrates how to calculate the volume of each prism separately before adding them together for the total volume.

## Want to join the conversation?

- Does the order I multiply the width, height and depth matter to find the volume?(20 votes)
- No, the order of multiplication of width, height, and depth does not matter, because multiplication is commutative and associative.

Have a blessed, wonderful day!(29 votes)

- i still don't understand it will someone please help me?(20 votes)
- Okay.

Sometimes you want to know how much space a 3d shape takes up. Now maybe you know how to figure out how much space a box takes up, or a pyramid, or a cylinder or something - but then somebody gives you some weird L-shaped thing! What do you do?

Well, you can look at the weird object, and realize that it's kind of like if you stuck two boxes together. And if you can figure out how big those boxes are, you can just figure out their volumes, add those volumes together, and you've got the volume of the bigger object.

It's about taking a big problem and breaking it into smaller problems that you can solve easier.(21 votes)

- I still don't get it and why so many steps.(14 votes)
- What I'm doing is multiplying the length, width, and height of the two forms (
). I'll find the volume by doing this. Next I'll add both the volumes together and find the volume of the irregular form.**it may be one**(13 votes)

- i dont understand this stuff its really hard(13 votes)
- just multiply length times height and widith(13 votes)

- I don't understand. But after the video I understand it a little(15 votes)
- I do not know what you are talking about can you help me more because I am only in 4th grade so I do not know this at all(11 votes)
- All you need is multiplication, you take the dimensions(length width and height) and multiply it together. For example, with a shape that is 2 inches tall, 5 inches wide, and 3 inches long, you would multiply 5x3 to get 15, then multiply 15 by 2 to get an answer of 30 cubic inches.(5 votes)

- Hey I don’t get it(4 votes)
- how would you find out the middle part??(3 votes)
- ie theenk yoo mooltiplie or sumtheeng(0 votes)

- so what square or thing do you want to times first?(2 votes)
- I still don't really understand it and what is a cubic cm(2 votes)

## Video transcript

- [Voiceover] Let's see
if we can figure out the volume of this figure over here. They've given us some of the dimensions. We see this side over
here is two centimeters, this is seven centimeters,
this is 12 centimeters, this is five centimeters,
this is three centimeters. And so like always, pause this video and see if you can figure it out. Well there's a bunch of ways to do this, but the way I'd like to do it is just to break it up into
two rectangular prisms. So what I'm gonna do is, in fact most of the reasonable ways to do this would be to break it up
into two rectangular prisms, and the ones that jump out at me is one prism like this that is three centimeters wide, five centimeters high, and then it is seven centimeters long, or seven centimeters deep. So this one right over here. And if this part right over here was transparent you would
see it look just like this. You would see it look just like this. And so this one once again, it is three centimeters wide, seven centimeters long. So this distance right over here is going to be the same as
this distance right over here. So seven centimeters long. So the width times the length times the height is five centimeters. Gets us to, let's see. Three times seven is 21, times five is equal to, 20 times five is 100,
one times five is five. So it's going to be 105. We can say 105 cubic
centimeters, cause you have centimeters times centimeters
times centimeters. So this blue part right over here, this blue rectangular prism, has a volume of 105 cubic centimeters. So now we can separately
figure out the volume of what I'm now highlighting
in this magenta color. What I'm highlighting
in this magenta color. If this was transparent, you would see this part back over here
and right over here. So what are its dimensions? Well, we know its height
is two centimeters, we know that this
dimension right over here, I guess you could say its depth, we could call it that,
is seven centimeters. But what is this right over here? If we want to consider
this, maybe it's length, or maybe it's width, depending on what we want to call it. Well, let's see, this whole
thing is 12 centimeters, from here to here is 12 centimeters, and we know that from here
to here is three centimeters, so this piece right over here
must be nine centimeters. So that must be nine centimeters, is this distance right over here. So the volume of this magenta part is going to be nine centimeters
times seven centimers times the height, times two centimeters. Which is going to get us, let's see, nine times seven is 63,
63 times two is equal to, 60 times two is 120,
three times two is six, so it's 126 cubic centimeters. So the total volume of the entire thing is going to be the volume
of the magenta stuff, which is 126 cubic centimeters, plus the volume of the blue stuff, plus 105 cubic centimeters. And that's going to give
us, for the entire figure, six plus five is 11, so one plus two is three, that's really one ten plus two tens is three tens. And then 100 plus 100 is 200, so we get 231 cubic centimeters is the volume of the entire thing. Fascinating.