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## 5th grade (2018 edition)

### Unit 5: Lesson 2

Finding volume- Volume of a rectangular prism
- Volume of rectangular prisms
- Volume in unit cubes by decomposing shape
- Volume through decomposition
- Decompose figures to find volume practice
- Decompose figures to find volume (unit cubes)
- Decompose figures to find volume
- Volume word problem: water tank
- Volume word problems
- Volume of rectangular prisms review

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# Volume in unit cubes by decomposing shape

Find volume of a rectangular prism with labeled side. Find a missing side length on a rectangular prism when given the volume.

## Video transcript

- [Voiceover] So these are two
pictures of the same figure. This is a front view of the object, and this is the back view of the object. And if a unit cube looks like this, what I want to do is I want
to figure out the volume of this figure in terms of unit cubes, or in terms of cubic units. I encourage you to pause the video and think of it on your own
before we try it together. All right, well, there's
a bunch of ways that we could tackle this, all of them kind of breaking this figure up in different ways. One way we could do it, we
could break it up into this. I guess we could call
it a rectangular prism. So, if you could see through there, it would be like this, so
this piece right over here, this piece right over here. And I'll redraw it here,
so you can visualize it. So, if I were to redraw
it, it looks like this. It looks like this. And what are its dimensions? Well, its four units wide. It's two units high. And then it's four
units, we could say long, or four units deep. So just like that. So what's the volume of this yellow part? Well, the volume is just you multiply these three dimensions,
the length times the width, times the height. So the volume is going to be our length times our width times our height. Four times four is 16 times two is 32. But we're not done. That's just the volume
of this yellow part. We still have to take into
consideration the volume of this piece right over here that we haven't figured out yet,
this piece right over there. Now, this one might just jump out at you. You could just count the unit cubes, but I'll redraw it here, just to show you what's going on. All right. So it looks like this. It looks like this. And what are its dimensions? Well, it's two wide, two high, and we could say one deep or one long. So its volume is going to be equal to your length times your
width times your height, which is equal to four. And you just see that. There's one, two, three, four
unit cubes in this object. So the total volume is going to be 32 plus 32 plus four is equal to 36. Now, of course, there's
other ways to tackle it. You could just say, hey,
let's figure out the volume of the blue layer
and then just double it because that red layer has the same volume as the blue layer. And the blue layer, you
could, say, well, look, it's only one deep. So we just have to
count the cubes up here, and then we'll know how
many unit cubes fit into it. So you literally could
just count one, two... Let me do it a color you can actually see. You just have to go one,
two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18. So you see there are 18
cubes in the blue layer, and there are going to be
another 18 in the red layer, plus 18, that also gets
you to 36 unit cubes, or a volume of 36 cubic units.