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Which is the best mathematical definition for volume?

This shape was made using 1 centimetre unit cubes. What is the volume of this shape?

The volume of one cube is 1 cubic metre. What is the volume of this cuboid?

Can you use 16 unit cubes to make a larger cube?

This cuboid was made out of cubes of 1 cubic centimetre. The cuboid has been partly painted. What could the volume of the cuboid be?

Counting Cubes 2

﻿Hello. My name is Mrs. Buckmire and today, I'm going to teach you about volume of cuboids. So first, make sure you've got a pen and paper. Remember, pause the video when I ask you to, so to complete tasks, but also whenever you like, if you feel you need a bit more time. And also remember, you can rewind as well so that you can hear something again. It sometimes just helps your understanding, okay? Let's begin. So before you all try this, I want you to write down how many cubes are used to build each of these cuboids. And how many different ways can you describe the size of these cuboids? Pause the video and have a go. Okay, so how many cubes are used to build each to these cuboids? Let's quickly count them. So for the first one, we have one, two, three, four, five, six, seven, eight. So there are eight and we know well, there're eight cubes. And here, we've got one, two, three, four, five, six in the top layer and then six in the bottom layer. So six times two is 12 cubes. And what about here? We've got one, two, three, four, five, six, seven, eight, nine, so nine here in this layer and then nine again here, and nine again here, so I get 27 cubes. Now, maybe you're doing a different method, that's fine. How many different ways to describe the size of these cuboids? So we actually know, let's say each cube is a one-centimeter unit cube where you could actually use and say oh, this one's 12 centimetres cubed, eight centimetres cubed and 27 centimetres cubed for size. What other sizes do we know? Good, what a length? So we could say this one is three across. Two up. And two backwards. Yeah? Maybe if you used the centimetres, you might have said this one was like four centimetres length, one centimetre maybe height. And two centimetre width are common terms used as well. So different ways to write the size. You could say this pink up here is smaller than the other two. That's describing size as well. So well done if you had a go. So let's start to connect that learning. So Binh and Xavier are finding the volume of this cuboid. What was volume again? Volume is how much space is taken up and if I tell you that each cube is a one-centimeter unit cube, they're going to show you how they found the volume. So Binh did 18 times three. Xavier did nine times six. Now, firstly, are they both correct? Do you get the same answers? 18 times three. So eight times three is 24. 10 times three is 30. So she gets 54 centimetres cubed. Xavier, nine times six is 54 centimetres cubed. So they are the same answer. So I assume they are correct. So where's this 18 from? Okay, so this length here is six cubes long and going across is three. Where does Xavier and why three lots? Well, there's one layer, two layers, three layers. So if I go like this, that is three layers. How about Xavier? Where was the nine from? Good, so three times three at the front equals to nine. And then the six, there's six lots, so there's one, two, three, four, five, six. Six. So if it was a painted cuboid of the same volume, what would the volume be? Yeah, it would still be 54 centimetres cubed. So what information would we need to be given? Yeah, we need to know that while the height is three centimetres, we'd know that the width is six centimetres and this length is three centimetres, using Binh's method. And Xavier's really is the same, isn't it? So he said oh yes, this is six centimetres. Three centimetres. And three centimetres. So exactly the same. The only difference is that Xavier kind of found this area first and then timesed it by the length. And Binh found this area first 'cause this is also three, remember, and then timesed it by the height. So both the exact same method but both get the answers or just different strategies. So a quick check. I want you to find the volume of this cuboid. Pause if you need more time. Okay, so I am going to find the area of this and then I'm going to times it by this height. So eight times four equals to 32. And 32 times two equals to 64 centimetres cubed. So this is my answer. Well done if you got that. What about this cuboid? Find the volume. Be really careful. Okay, so what I would do is I'm going to find the area of this, so I have five times three, which equals to 15, and then I'd times it by this length here. So 15 times four equals 60 centimetres cubed. Well done if you got that. Did some people get these much bigger numbers? Did you multiply it by extra dimensions? So that's why it's really important you think about what you're doing. So really, we want this kind of area of the face times the length. So you could have also done the area of this one. So five times four and then timesed it by three, so 20 times three is 60. But we don't just want to multiply all the things together. So some people like to think of it as length times width times height. But then you need to be careful oof what information is given and making sure you're using the right numbers. Okay, let's apply this to the independent task. So this is a bit of a challenge. I thought I'd make it more interesting. Each cuboid has the same volume. And I want you to find the missing length. So you just had a go at finding volume. So I know you know how to do it. You're great at that but now I want you to find the missing lengths. Now, if you think I'm up for the challenge, I know what I'm doing, pause, have a go. Otherwise there is support. Okay, so for your support, each cuboid has the same volume, find the missing lengths. Now, only one of them has enough information for us to find the volume 'cause you might be looking at this like how can I find the, I know it's same volume but I do I work it out? There is one you can work out the volume of and that is that one. So we can find the area of this front face here. So 12 times 1/2. That's the same as 12 divided by two, which is six. And then we times it by 20. So the volume of this one is 100 and, yeah. Okay, so now, to find out the missing lengths, first, maybe even label what length is missing and then have a think. So for example, here, I know this one's five, this one's eight. So I can imagine, well, not even imagine, I can work out this area of this space and then I just need to work out this missing length. Maybe you need to do some dividing. I'm going to stop there. I think you can do this. Pause the video and have a go. Okay, so we already looked in the support that here, we find this area first. 12 times 1/2 was six and six times 20 meant 120 centimetres cubed. And I said I could find this area of this face by doing five times eight equals to 40. And I want to know this length. And now I know that 40 times the length equals to 120. So I'm going to do 120 divided by 40 and I get three. So this missing length is going to be three centimetres. Okay, here we know this. We don't have the height. So four times six equals to 24. And now to get this, I want to know how many times I have 24 to get to 120. So you could count up if you weren't sure or you can divide. So I would do 120 divided by 24 equals to five centimetres. But it's fine if you counted up 24, 48, et cetera. Last one, have you done it? If you didn't do it, pause and have a go. If you got all of those wrong, have a go now. Let's see if you've understood. Okay, so here, this area is 15 times four equals 60 centimetres squared and now I want to know this missing length. So how many lots of 60 centimetres squared so I need to get to 120? Two. So two lots, this is two centimetres. Right, well done if you got those answers. Okay, so look at the explore. Yasmin puts one-centimeter cubes into this box. How many cubes can she fit in? What other boxes can she fit her cubes in? Pause if you're confident, support in a moment. Okay, so for support, all I want to give you is a box. Now, first, you know how many one-centimeter cubes fit in here because you know how to find the volume. Rewind back if you're not sure but I think you can find the volume of that and then that tells you how many cubes you can fit in. So that answer you have got it. What other boxes can she fit it in? Well, why don't you just label a box randomly. So let's say if this is six centimetres, then what would this length be and what would this one be? So have a think. If that was six and maybe this length will then tell you what this area is. It tells you how many cubes in that top layer and then you can see how many more layers do you need to get to that? Have a little go. Yeah, just have some fun with it. Have a go. Just try out random numbers. Hopefully some of them might work. You know I'm going to give you an answer in a moment but do have a go first. Okay, so we said that to find out how many cubes you can fit in, we need to know the volume. So we know this is three and this is three, so this, there are nine and there's two layers, so nine times two is 18. So we could do two times three times three equals 18 centimetres cubed. What other boxes can she fit her cubes in? Okay, so this is more similar to one that I went for in support. So I said this was six centimetres and I said that you need to work out this and this. So let's say if you said oh, this one could be three centimetres. So six times three is 18, so each layer has 18. She only have 18 cubes. In fact, this answer shouldn't be centimetres cubed, it's 18 cubed she can fit in, she wants to know how many. Check your work. This is why you have to check your work. So back to this. So we have six times three is 18. Well, she's got 18 cubes so they just must be one centimetre high. So the box would be six by three by one. Okay, I've done another little one here and I've said that the height here is one centimetre. I've just made it really small. So let's say the length then is 18 centimetres so that means 18 times one is 18. So that means the width of one of the cubes is also one centimetre, okay? So really, this is about factorising 18 in different ways to factorise it into three parts. So well done if maybe you got some different answers. Check them really carefully to make sure you multiply the different dimensions, they are equal to 18 and that you're actually labelling the right dimensions as well. Well done. If you had a go at all the try this, the connecting work, the independent work, the explore, then I think you've done really, really well today. If you'd like to share your work, ask a parent or carer to do it on Instagram, Facebook or Twitter. Tag @OakNational and #LearnwithOak. I'd love to see your work as always and do the exit quiz. That's when you really get to show off what you understand and just kind of test your own knowledge. You don't really know if you know something until you test it out. Okay, have a lovely day. Bye.

Congratulations on completing the lesson. Good luck on the quiz!

What is the volume of a cuboid with lengths 4cm, 2cm and 5 cm?

Which calculation could you use to find the volume of this cuboid?

Work out the volume of this cube.

The volume of this cuboid is 120 cubic centimetres. Work out the missing length.

Is it true or false that to find the volume of a cuboid you always just multiply all the given numbers together?

A net has been drawn on a centimetre grid and filled to make a solid cuboid. What would be the volume of the solid cuboid?

Cuboids

In this lesson, we will learn how to calculate the volume of a cuboid.

Maths

Y8 Maths

Key Stage 3

Year 8

Volume and surface area of prisms

Geometry

THEME

UNIT

3-D Shapes

Prisms and cylinders

Nets of cubes

Nets of prisms

Counting cubes (Part 1)

Counting cubes (Part 2)

Volume of prisms and cylinders

Surface area introduction

Surface area conjectures

Surface area of cuboids

Surface area of cylinders

Is it true or false that this shape has the same number of edges as vertices?

Yasmin says this is a prism because the top face and bottom face are both rectangles. Is this shape a prism?

Lesson overview:Cuboids

Core Content

Volume and surface area of prisms: