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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.

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  • piceratops tree style avatar for user cbor
    is there such thing as 4-d?
    (37 votes)
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  • duskpin seed style avatar for user #CrazyAboutMath
    Can you please post a video on how to find the volume of an irregular rectangular prism? Thanks very much.
    (25 votes)
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  • piceratops seedling style avatar for user lamor stewart
    can you multply a diffrent way
    (13 votes)
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  • winston baby style avatar for user tadesezewudu
    can we do like this , total volume= 2x6x4 =48 ,then 3x2x2=12, so 48-12=36 ?
    (12 votes)
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  • aqualine ultimate style avatar for user ashwinich412
    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)
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  • aqualine ultimate style avatar for user rproper2029
    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)
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    • primosaur seed style avatar for user Ian Pulizzotto
      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)
  • starky sapling style avatar for user jorgeo1010
    - [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)
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  • starky seedling style avatar for user KaidenB
    Can you Choose what to multiply on a shape or do you have to start with the same length?
    (3 votes)
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  • aqualine seed style avatar for user Myangel
    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)
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  • blobby green style avatar for user sowmyaregatti
    whats a 4 by 4
    (2 votes)
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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.