Video: Properties of 3D Shapes

In this video, we will learn how to analyze 3D shapes to see what features a shape always has and what features it sometimes, or never, has.

17:04

Video Transcript

Properties of 3D Shapes

In this video, we’re going to look carefully at 3D or solid shapes to see what features a solid shape always has, what features it sometimes has, and what features it never has. Wait a moment! What’s going on here? This isn’t right. This shape isn’t a cylinder, is it? It’s a cuboid, but how do we know it’s a cuboid? What makes a cuboid a cuboid? And what makes a cylinder not a cuboid? Answering questions like this is really important because if we want to be able to spot a cuboid every time we see one, we need to know the sort of things to look for.

Now, there are three words that we can use to help us, and these are the words “always,” “sometimes,” and “never.” How are these words going to help us? The cuboid in our picture is blue. Can we say cuboids are always blue? Remember, the word “always” means every single time. We can’t say this it all, can we? Here’s an orange cuboid and a red one. Cuboids can be any color at all. This one is covered in pink splotches, but it’s still a cuboid. We can’t say cuboids are always blue, but it is true of them some of the time. They are sometimes blue. The color of a 3D shape isn’t what makes it that shape, and the same is true of the size of a shape.

At the moment, our cuboids are around about the same size. Can we say cuboids are always the same size? Not at all. Look at this tiny green cuboid we’ve drawn at the top. Once again, this is another “sometimes” fact, isn’t it? Cuboids are sometimes the same size. And the size of a 3D shape, again, isn’t something that makes it that type of shape. And the position of a shape isn’t important either. Cuboids are only sometimes in this position. But if we turn them, they don’t stop being cuboids, do they? Just like you don’t stop being you if you stand on your head.

We can say that a shape’s color, how big it is, or what position it’s in are not really important when it comes to identifying a 3D shape. What really matters are the things that are always true of a 3D shape. As we’ve said already, when we use the word “always,” it means every single time. What makes the shapes that we can see cuboids are the things that every single cuboid has in common. And with 3D shapes, this means looking at things like the number of faces or flat surfaces that a shape has, also the number of edges and vertices or corners.

This cuboid has six faces. Now, because it’s a solid shape, it’s quite hard to show this on a video. So what we’ll do is we’ll put some dotted lines in to show what the back of the shape looks like. There we go. That should help. Now, if we count the faces, we know there’s one on the front and another one at the back, so that’s two. There’s one at the top and another one at the bottom, so that’s now four. And there’s one on the left and one on the right, six faces altogether.

Do cuboids always have six faces? Let’s put our dotted lines in, and now let’s count the faces. One, two, three, four, five, six. We can say that all cuboids have six faces. Not only that, but if we look at the shape of each face, they’re all rectangles, aren’t they? We could use this to make another “always” statement. All faces are rectangular. And if we count the number of edges or vertices, we’d also find some more rules that make cuboids cuboids. For example, all cuboids have one, two, three, four, five, six, seven, eight, nine, 10, 11, 12 edges. Without 12 edges, these wouldn’t be cuboids. And this is where we can use the idea “never.”

We could use our “always” statements to help write some “never” statements. If we know all cuboids have 12 edges, then we can say cuboids never have less than 12 edges. And if we know that all cuboids have six flat faces, then we could say cuboids never have any curved surfaces. If we’re going to be shape detectives trying to find out the names of 3D shapes, we don’t want to be looking at the color, the size, or the position of the shapes. We want to be looking at the things that are always true of shapes in this group, things like the number of faces, the number of edges or vertices. Let’s answer some questions now where we have to think about the properties of 3D shapes. And we’re going to keep in mind these ideas of “always,” “sometimes,” and “never.”

Chloe sorted these shapes into two groups. How did she sort the shapes? Are all the cylinders in the same group?

In this question, we’re told that Chloe has sorted some shapes into two groups, and we can see pictures of them: group 1 and group 2. Can you see that these are 3D shapes? They’re not flat, are they? They’re solid. In the first question, we need to look at what rule Chloe’s used to sort out the shapes. How did she sort the shapes? Did she sort them by the type of faces they have? Well, it doesn’t look like it, does it? Because there are shapes with flat faces in both groups. And there’re also shapes with curved surfaces in both groups.

All of the shapes in group 1 are different, so it can’t be anything to do with a particular type of shape. There’s only one thing it can be, and it’s probably the thing you notice straightaway. Chloe’s put all the green shapes in group 1 and all the blue shapes in group 2. She sorted the shapes by color, and we know that the color of a shape isn’t a very important feature. Any shape can be any color. And that’s why there are different types of shape in group 1. And there are also different types of shape in group 2.

Our second question asks, are all the cylinders in the same group? Let’s remind ourselves what a cylinder is. Can you see one in group 1? A cylinder has two flat faces, one at each end. But it also has a curved surface that goes all the way around. Can you see any more cylinders that Chloe sorted? This shape here is on its side, but it has two flat surfaces, one at each end, and a curved surface all the way around.

The cylinders are not all in the same group, are they? And we know this because Chloe has sorted the shapes, not using something important, but just using their color. So the same shape can be in different groups. Chloe has sorted these 3D shapes by color. And because the color of a shape isn’t what makes it that type of shape, all the cylinders are not in the same group. The answer to the second question is no.

Complete these sentences about cubes. All cubes what. Are blue, are big, or have 12 equal edges? But not all cubes what. Have eight vertices, are pink, or have six faces?

In this question, we’re being asked to think about a particular type of 3D shape, the cube. And we’re given some pictures of some cubes to help us visualize them. It’s always useful to see a picture or to actually have a cube in our hands when we’re answering a question like this.

Now, we’re given two sentences about cubes to complete. And there’s one big difference between these sentences. Can you see it? The first sentence is a sentence that’s about all cubes, in other words, every single one, all the ones in the pictures, every cube you’ve ever seen. But our second sentence isn’t about every single cube, it says “but not all cubes.” When we say not all, we mean some. This is going to be a fact that’s only sometimes true about cubes.

Let’s look at our first sentence to begin with then. How can we finish the sentence so that it’s true of every single cube? Can we say all cubes are blue? Well, of course, we can’t. In this picture, we can see a pink one and an orange one as well as a blue one. An ice cube is transparent. A sugar cube is white. Cubes can be any color at all, can’t they? The color of a shape isn’t what makes it that type of shape.

What about the size of a shape? Are all cubes big? Well, we can look at these cubes and we can see they’re all different sizes to begin with, can’t we? But even if you thought these cubes were all big, stand up and walk to the other end of the room and carry on looking at your screen. If you’re a long way away from your screen, these cubes are going to look quite small, aren’t they? But they’re still cubes. We can’t say all cubes are big or all cubes are small. The size of a cube isn’t what makes it a cube.

So we’re only left now with one possible answer: all cubes have 12 equal edges. The edges of a 3D shape are those parts where two faces meet. So if we take a look at our orange cube, this line here is an edge. Let’s count the edges on our cubes. One, two, three, four. Can you see we’ve made a square shape of edges? Well, there are four edges just like this at the back of our cubes too.

We can’t see them all, but what we’ll put some dotted lines so you can see what we’re talking about. So another four edges makes eight edges, and there are another four edges front to back. Four, four, and another four makes 12. And this is true of every cube you could ever see. Did you notice the word “equal” in this phrase too? Each of the edges is the same length. This is why we can turn a cube in lots of different directions and it can still look the same. All cubes have 12 equal edges.

But not all cubes what. Can we say that not all cubes have eight vertices? Remember, the vertices of a shape are its corners. And on a 3D shape, this is where two or more edges meet together. Imagine you are making a cube out of blobs of plasticine and matchsticks. The vertices would be the number of blobs of plasticine that you need. In other words, it’s where your matchsticks meet together.

Now, if we look at our corners on our middle cube, we can see that there are one, two, three, four at the front and another one, two, three, four at the back. There are eight vertices, but we know that the number of vertices is actually something that all cubes have in common. This phrase could actually be used to finish the top sentence. All cubes have eight vertices, not some cubes.

Can we say some cubes are pink? Well, as we’ve said already, cubes come in all sorts of colors. We can definitely say not all cubes are pink, so we know how to complete this sentence, don’t we? Let’s just check our last fact. Can we say not all cubes have six faces? Think for a moment of a dice, it has a different number on each face. And if it’s a cube, what do the numbers go up to? They go from one to six, don’t they? Because each cube has six faces.

This is another fact about cubes that we could have used with the first sentence. All cubes have six faces. In this question, we thought about properties of cubes that are always true — in other words, the sorts of things that make a cube a cube — and the things that are sometimes true. All cubes have 12 equal edges, but not all cubes are pink.

There is a mystery shape in this bag. Choose from the following clues the one that will not help you guess the name of the shape. It has a curved surface. It has two flat faces. Or it is small. Based on these clues, what is the shape in the bag?

And then we’re given three pictures of 3D shapes to choose from. How good are you at identifying 3D shapes? And what if you can’t see them? We’re told that there’s a mystery shape in this bag, and we can’t see it, can we? Now, we’re given 3 different clues to help us identify the shape. It has a curved surface, it has two flat faces, and it is small. Now, all three of these clues are true of our shape, but they’re not all helpful. We’re told to choose from these clues the one that’s not going to help us guess the name of the shape. Can you spot which one it is?

What are the sorts of things that we look for if we’re trying to work out the name of a 3D shape? Well, things like whether the shape has a curved surface or not and the number of faces that it has. That’s important too. These are the things that make a particular type of 3D shape, that shape. But if we look at our last clue, it’s talking about the size of the shape.

Now, if I said to you: “I’ve got a mystery shape that I want you to guess. It’s small. What do you think it is?,” you’d say to me: “That’s not enough information. Any shape could be small.” The size of a shape isn’t a property that we use when we’re trying to identify 3D shapes. Some shapes are big. Some shapes are small. Some shapes are somewhere in between. The clue that’s not really going to help us guess the name of the shape is it is small.

In the last part of the question, we need to identify the shape. Based on these clues, what is the shape in the bag? And we’ve got three possible shapes to choose from. Do you know the names of them? The blue shape is a cone. And we can see that that’s got a curved surface, but then so has our second shape, which is a cylinder, and also our third shape, which is also a cylinder. Our second clue tells us that the shape has two flat faces. Now, if we look at our first shape, we can see that it has a flat face at one end. But at the other end, it goes to a point. So this only has one flat face. This isn’t the shape we’re looking for.

But our second shape does have two flat faces. Cylinders have a flat face at either end, don’t they? Because our last shape is a cylinder too, we can see its two flat faces as well. So we know the name of the shape is a cylinder. But do you know what? To identify the actual shape that we’re talking about, we need to use that unimportant clue. Only one of our cylinders is small.

To guess the name of a shape, we don’t need to know its color, its size, or what position it’s in. And so the clue that was not going to help us guess the name of the shape is “it is small.” But once we’ve worked out that the shape was going to be a cylinder, we used all three clues to find that the shape in the bag was the green cylinder.

What have we learned in this video? We’ve learned how to look carefully at 3D shapes, to see what features a solid shape always has, sometimes has, and never has.

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