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

Lesson 3: Decompose figures to find volumes# Volume in unit cubes by decomposing shape

Explore the concept of decomposing complex shapes into simpler ones to calculate volume. Understand volume as additive and how to use multiplication of length, width, and height to find the volume of rectangular prisms. Learn how you can approach the same problem differently.

## Want to join the conversation?

- is there such thing as 4-d?(36 votes)
- Yes, the 4th dimension would be time. 4-D is mainly used in Sciences like Quantum Physics or something that evolves the space-time dimension.(43 votes)

- Can you please post a video on how to find the volume of an irregular rectangular prism? Thanks very much.(26 votes)
- can you multply a diffrent way(12 votes)
- there are many ways to multiply like traditinal and lattice and i prefer lattice, so yes.(6 votes)

- can we do like this , total volume= 2x6x4 =48 ,then 3x2x2=12, so 48-12=36 ?(11 votes)
- Yes good question anyway(2 votes)

- Why isn't there a thing called 5-d, 6-d, and more. Why only 1-d, 2-d, 3-d, and 4-d?(6 votes)
- Hypothetically, it goes up to Infinity-D, but we don't want to overcomplicate it. Our world only goes up to 3-D, so working on trying to figure out 4-D is already a
*HUGE*step in science.(9 votes)

- As an Englishman i have never heard someone say "four hundred five thousandths" and that just sounds very strange to my ears. Here you would say "four hundred and five thousandths". I'm not sure if this is a dialect difference in America or whether this is an actual mistake on the site?(3 votes)
- At least in America, the two phrases have different meanings! The word "and" is like a decimal point, separating the whole number part from the fractional part.

"Four hundred five thousandths" means 0.405.

"Four hundred and five thousandths" means 400.005.

Have a blessed, wonderful day!(14 votes)

- - [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.(4 votes)
- Can you Choose what to multiply on a shape or do you have to start with the same length?(3 votes)
- i don´t get why you have to do all this extra work when all you have to do is count the cubes bye two.like whats the point?(3 votes)
- because it is eaisir(1 vote)

## 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.