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## 7th grade foundations (Eureka Math/EngageNY)

### Unit 6: Lesson 4

Topic E: Foundations- Volume through decomposition
- Decompose figures to find volume
- Volume word problem: water tank
- Volume of a rectangular prism: fractional dimensions
- Volume with fractions
- Volume of a rectangular prism: word problem
- Volume word problems: fractions & decimals

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# Volume through decomposition

Sal finds the volume of an irregular 3D figure by breaking the figure into 2 rectangular prisms and finding the volume of each part.

## Want to join the conversation?

- imagine using khan academy in 2022,(plz up vote my comment so every one can see it, thanks)(32 votes)
- imagine cant be me(6 votes)

- very helpful very help very helpful (please up vote so peeps see:)(20 votes)
- I freaked out when I got an irregular shape homework but after I watched this video, I did perfectly on it. Before the video, I thought that I had to add the numbers together but when I watched the video, I understood that I had to break the irregular shapes apart and multiply the length,width, and height to get the volume and add both of the shape’s volume to get the answer.(14 votes)
- i still don't understand it will someone please help me?(9 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.(6 votes)

- Does the order I multiply the width, height and depth matter to find the volume?(7 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!(8 votes)

- If common sense is so common, why do so few people have it?(8 votes)
- How do you measure how many people have common sense? I assume you are interpolating from what you think common sense means. The other issue is that we are often a reactionary people rather than a proactive people. Reactions often go aganist common sense while proactive uses more common sense.(4 votes)

- i dont understand this stuff its really hard(7 votes)
- just multiply length times height and widith(4 votes)

- I don't understand. But after the video I understand it a little(8 votes)
- I still don't get it and why so many steps.(6 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**(4 votes)

- This is so easy but my friend things it so hard and I'm only in fourth grade. Can we have a face reveal to?! (Please put votes so everyone can see this, Thanks a lot.)(6 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.