Which formula works out the volume of a prism?

What is the volume of this shape?

The perpendicular height to the 6cm base is 8cm. Which calculation would correctly give you the volume of this prism?

Work out the volume of this triangular prism.

Work out the volume of this cylinder.

This cuboid has a volume of 45 cubic centimetres. What is the missing height?

Volume of Cylinders and Prisms

﻿Hello, my name is Mrs Buckmire. And today I'm going to be doing a little lesson with you on: Introduction to Surface Area. Now first, make sure you've got a pen and paper and try and clear away any distractions as well, to make sure that you are focused. If you need to pause the video at any time, please do. Also, please pause when I ask you to 'cause it just means that I want you to have a go at something and have a bit of a think, I want you to have that time. Also if you need to rewind the video, please do. If you need to hear something again, it's a really useful way to kind of better understand something, it's just hearing it again sometimes. Let's begin. So if we'll try this. So looking at these three shapes, what's the volume of them? Can you work it out? Yeah. Each of them have six unit cubes, so all of them have the same volume. Now, what I want you to do is tell me how many faces will be visible on each shape and for each shape, can you sketch a shape with the same number of visible faces, but a different volume. Now just quickly by faces, I mean, for example, here, this bottom one has one, two, three, so three of the unit cubes faces shown, okay. So then you have to, as you work up all the others, how many faces are shown are visible on each shape? Okay. Hopefully that makes sense. Pause the video and have a go. Okay, so for this first one, so I already said, so the front has three, one, two, three, the back also has three, let's do it all, track it. And the top has four. And the bottom also has four looking from this left hand side, looking that way has one, two, three, four as well. And looking that way has four too. So you kind of got to visualise it from different sides. So all together I get three plus three is six plus four is 10 plus four is 14, plus four is 18 plus four is 22. So there are 22 faces that are visible. If you weren't sure and that has now helped, feel free to pause. Okay, so for this one, did you get, so I see looking from the top, I can see six. And that means from the bottom I would also expect to see six, from this side, I can see three, this side, three as well. And from the front, I can see two and two, so 12, 15, 18, 20, 22 as well. And for the final one, you should get 26 faces. So now trying to sketch a shape with the same number of visible faces but different volume. I think this was a pretty difficult task. So the first one, I did this, so I just thought, okay, a straight stick. And I just kept adding until I got to 22 faces. So you see from the top, there are five and actually the left hand side, right hand side and bottom's also all five to get to 20. And then either ends gets me to 22. Now the next one you might just done the exact same shape, but I want to be a bit creative. So I did another one here. Now you can see from the top, we can see one, two, three, four, and it's the same from the bottom, from the left hand side, I know I can see one, two, three, four, five, and the right hand side is also five. From the front I can see two, I'll put it up here and from the back also two. So four, eight, 12 plus 10, 22. So its 22 faces. And for 26 faces, I got this. Feel free to pause and check I'm correct. If you got something different, well done, there are plenty of different answers. Oh, and remember, they all had to have a different volume, so let's just clarify that. This one had one, two, three, four, five units cubes were used. This one was one, two, three, four, five as well. And this one was seven, so none of them were six. So that's why it was okay. Okay, so surface area. What if I told you, you already know how to work out the surface area? I'm yet to introduce it but you already know it. You just found the surface area of things like this. It's by counting the faces you're seeing, the area of the surfaces, the surface area of this 3D shape. What was this one again? I've actually already forgotten. Four, eight, was it 22 as well? Yeah, it was, wasn't it? So it was 22. So if they were unit centimetres cubed, it's 22 centimetre squared, 'cause its the area. Okay, so for this one, the surface area would be the area of the surfaces. So you already know how to find the area of a triangle, the area of a triangle, the area of a rectangle, a rectangle, a rectangle and then you just add them all together. What is the point of this? Why do we find the area of surfaces? So it's related to sometimes if we want to paint a room, we want to know actually what the surface area we want to paint, also related to nets and boxes. So if we want to know actually we need to box something and we want to actually, how much material do we need for that box. Then we need to know surface area, okay. So area is a measure of 2D shapes. So we can find the area of the faces. And this is referred to as surface area and that's the main thing I want you to remember and learn from this lesson. Okay, So four independent tasks. Binh says this solid has a surface area of 15 centimetres squared, but she is incorrect. What is the correct surface area? What mistake do you think she has made? And also for the second question, what is the surface area of this solid? Where could you add a cube to make the surface area 40 units squared, okay? Pause the video, the questions are on the worksheet as well. And have a go. Okay, let's go through this first one. So the correct surface area, where if I think about from the top, I can see one, two, three, four, five, and from the bottom also five, from the front, I can see one, two, three, four, five, six, seven, eight. And from the back, I can also see two, four, six, eight. From the left hand side, I'll be able to see one, two, three, four, and the right hand side, I'll be able to see one, two, three, four. So if I add these together I get 10, 18, 26, 30, 34. So it should be 34 centimetres squared. So what mistake do you think she made? If I maybe do it in yellow, she got 15. So one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15. Maybe she just missed out the ones that you couldn't really couldn't see clearly. And she also missed out these ones. I'm not sure what she did wrong. Maybe you've thought of a different mistake, but just make sure you're not making that same mistake. Okay, what is the surface area of this one now. I've made it much bigger to help you 'cause I thought this was tricky. I put it in because I thought, Oh, this will make them think, okay. So I was thinking, so from the front, I can see there's one, two, three, four, five, six, so six. And then from the back then I can also see one, two, three, four, five, six. From the left hand side and right hand side is where it gets tricky. So I can see one, two, three, four from the left hand side. I can also see four from the right hand side. So I'll be able to see this one, this one, this one and this one down here, 'cause that will pop out from underneath here. So I can see four from the right hand side as well. We did top, bottom. Sorry we did front back, left hand side, right hand side. So from the top I can see one, two, three, four, five, six. So another six. And from the bottom, I'll also be able to see six, but that's not all of them, is it? We haven't yet included this one. So from inside, I can see this one and this too. And I also, haven't done from this side here. So one, two there as well. So now when we add those together, so 12, 14, sorry 12 plus four is 16 plus four that makes 20. And here I've got 12 plus two is 14 plus two is 16. And I have to add these together, all together. There's 36 units squared. Wow, that was a tough one! So well done, if you've got that. So where can you add a cube to make the surface area 40 units squared. Well it's got to be somewhere, which adds on four units squared. So let me use, I'll use purple. So I think if I add it on at the end, so I add it on here. Let me do a little drawing. So normally my cube has six faces. So I'd be adding on six units, but then because one is attached here, actually I'm only adding on five and from the original one, this one, which had a cross on it can no longer be seen as well. So I'm taking away one. So I'm adding on five taking away one. So I'm just adding on four, so it works out. And actually if you add them on to any end and add it onto the end there as well, or like instead, as long as it's only joining at one part up here as well, then actually it could work out if you've any of those answers. Okay, so for your explore, Zaki attaches eight of these unit cubes together. What is the maximum surface area? What is the minimum surface area? What do you notice? What if there are nine cubes? What do you notice then? Have a little play around. If you need some support, I'll give you some on the next slide, but pause the video now and have a go if you are confident. Okay, so just a bit of support. So Zaki attached eight of these cubes together. What I've done, I've actually just put them here. It might help with visualising. And I just want to touch them in different ways to create 3D shapes and then trying to find the surface area. Now, here are some examples. These are not exhaustive, these aren't all the examples. So there's not definitely the maximum, minimum example here. These are just ones, you can have a go finding the surface area, which one's got the greatest surface area. Do you think you can make one which has an even bigger surface area? Can you make one that has an even smaller surface area? Just have eight though. Pause the video now. Okay, so the maximum surface area I found was this one. So when it's all as a stick, because then I found that the surface area, so from the top left hand side, right hand side and bottom, I would get an eight. So eight times four, which is 32 and then you've got the front and back so 32 plus two, so I got 34 units squared as my largest surface area. Did you get higher? I'd be very impressed, but I don't think there is a higher and the reason why I don't think there's a higher, is when you're attaching each one, you want them to attach in the minimum points possible 'cause you want as many exposed, as many visible as possible. So if you just attach each one by one, then each time each lot of six, you are taking one away and then you're taking one from the other one as well. So that's why I think actually this is the best way. To get the minimum surface area, you want them to be attached to as many points as possible. So you kind of want them clumped together and that's how I got to this cube. So here I got the surface where it's a cube, every surface, every face of the cube is four. So four times six is the surface area. So I got the minimum being 24 units squared. Was your minimum higher? You didn't spot this one? Oh dear! What do you notice? There's loads of things you can notice. So you could notice, Oh, actually eight is a cube number. You can notice actually the stick is one with the maximum. Maybe you're thinking, Oh, maybe, oh, so even if there's nine cubes, maybe that will be the maximum as well. And I think you'd be correct. What is the minimum surface area? It's quite hard to work out with nine. Do you find that as well? So I found out actually, if I just stick it on here onto my eighth one maybe that's the best way? But I wasn't really sure. Hope you've had fun, just having a go and noticing different things. Really, really well done today. Today was kind of an introduction. You guys already knew how to do surface area but hopefully now you feel a bit more confident with it as well, okay. I would love for you to do the exit quiz. I think it would really help your learning. Just getting some feedback on your answers, I think is really useful. So do have a go and I'll see you next lesson. Bye.

Which statement is true?

This shape was made with 1 centimetre unit cubes. What is the surface area of this shape?

What is the maximum surface area of combining 10 of these 1cm unit cubes together?

Introduction to Surface Area

In this lesson, we will be introduced to the concept of surface area, and how to calculate it.

Maths

Y8 Maths

Key Stage 3

Year 8

Surface area introduction

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)

Cuboids

Volume of prisms and cylinders

Surface area conjectures

Surface area of cuboids

Surface area of cylinders

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

Work out the volume of this cube.

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

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:Surface area introduction

Core Content

Volume and surface area of prisms: