Video Transcript
Edges of 3D Shapes
In this video, we’re going to learn
how to identify and count the edges of 3D shapes. We’re also going to look at their
vertices too. And we’re going to learn how to
build shapes.
Now, when we use the word edge in
everyday life, we often use it to describe the boundary of a shape, the very end of
it, its outer limits. So, the edge of a field might have
a fence all the way around. It’s where one field ends and the
next one begins. If we drew a line around the edge
of this screen, it would show the boundary of where the video ends and something
else begins. Now, in this video, we’re
particularly thinking about 3D or solid shapes. And in maths, the edge of a 3D
shape has a certain meaning.
The edge of a 3D shape is where two
of its faces meet. Where they touch or meet, it forms
an edge. Let’s think about the edges of a
cube to begin with. Now, as we’ve just said, the edges
of our cube are going to be those places where two of its faces meet. Do you remember what the faces of a
3D shape are? They’re flat surfaces that make up
a shape. And the cube’s faces are all
squares. And we can only see three of the
faces on this cube, and they’re all green. So, it might be hard to know which
face we’re talking about. Let’s put some numbers on the faces
and turn it into a dice.
There we go. Now, to find an edge on our cube,
we need to choose any two of these faces. Let’s choose the one with the
number one on it and the one that has the number three on it. Can you see where these two squares
or faces meet? It’s this line here. This is one of the edges of our
cube. And if we look at the place where
the edge with the number three on it meets the face with the number two on it, we
can see another edge. There’s also an edge where the
number one meets the number two. In fact, all the black lines that
make up the picture of this shape are edges.
This brings us onto a question we
could ask ourselves. How many edges does a cube
have? Now, when we’re working with a
video like this, we’re working with pictures of cubes. We haven’t got a cube in our hands
to look at. But we have already said that the
black lines that make up the outside of our picture are the edges of the cube. How many can you see? There are one, two, three, four,
five, six, seven, eight, nine edges on this picture. But as we’ve just said, this is
just a picture. We really want to be able to turn
this cube around so that we can see the back too because there are some hidden edges
that we can’t see at the moment.
Now, this is where building a cube
can help us. This is the sort of thing you could
do if you had time. Firstly, you’re going to need
something long and thin, perhaps cocktail sticks or toothpicks. We’re going to use straws. And then you’re going to need
something squashy. You could use fruit gums or
marshmallows. Just in case we get tempted to eat
them, we’re going to use modeling clay.
Let’s start by making the base of
our cube. As we’ve said already, a cube has
square faces, so we’re going to need to make a square. Let’s pick up the straws and the
modeling clay that we need. There we are, one base of the
cube. We’ve used four straws and four
blobs of modeling clay to connect them at the corners or vertices. Now, we’re not making a 2D shape,
we’re making a solid shape, so we’re going to need to give it some height. Let’s use four more of our straws
to do this.
And now, finally, can you see what
we need to do to finish our cube off? We need to use our last four straws
and four blobs of clay to make a square on the top of our cube. And there we have it. Now, we could call this a skeleton
cube. Can you see why? Although it looks like a cube, it
doesn’t have any flat surfaces, does it? There are no faces to this
cube. If we wanted to, we could put our
hands straight through the middle of it.
But using the outline or the
skeleton of a cube like this is really helpful to us. This is because it shows us all the
edges and the vertices of the cube that we wouldn’t normally see because they’d be
hidden around the back. The straws in our model represent
the edges of a cube. Let’s count them to see how many
edges there are. And as we do, we’ll label them on
our green cube, too, so you can match the two up.
There are one, two, three. Wait a moment! How are we going to label this
edge? We can’t see it on our green cube
because it’s around the back. Well, there is a way to show that
it’s there but that it’s hidden away around the back. And that’s by using a dotted
line. Often, you’ll see dotted lines on
drawings of 3D shapes; it helps us to visualize what they look like. Let’s carry on counting from
three. Four, so that’s four edges that go
around the square face at the bottom, five, six, seven, eight, and then four more
that make up the square face on the top, so that’s nine, 10, 11, 12 straws that
we’ve used altogether.
Now as each store represents an
edge, we can say that a cube has 12 edges. And not just our green cube here;
every cube ever has 12 edges. Maybe you’ve got a building block
or a dice that you can look at and count. As we’ve said already, building
skeleton models like this are really useful because they also show us the number of
vertices that these shapes have. Remember that a vertex is where two
or more edges meet. And on our skeleton cube, these are
the blobs of modeling clay. There are four around the base of
the cube and another four at the top, which makes eight altogether. Cubes have eight vertices. And more importantly, for this
particular video, we also know they have 12 edges. And maybe you noticed on a cube,
all 12 edges are the same length.
Let’s look at another 3D shape. How many straws would you need to
build this shape? In other words, how many edges does
it have? Now, just like before, we can’t see
all the edges, can we? But we could think really carefully
about what this 3D shape might look like all the way around. And we could even draw in some of
the edges that we can’t see using dotted lines. What makes up this shape? Well, we can see a triangular face
at this end. We can’t see the face at the other
end, but we’d expect it to be triangular, too. And then, we have three rectangular
faces along the sides. There’s this one we can see. And then, there’s one on the bottom
and one hidden away around the side.
By adding the dotted lines, it
really helps us to visualize the shape, doesn’t it? Now, let’s use what we’ve just
found out to help build the shape. We need to make a triangle at one
end. So, that’s three edges, another
three edges for the triangle at the other end, and then three more edges to connect
them both together. This shape, which is called a
triangular prism, has nine edges. We’re going to need to use nine
straws to build it. And because we can see that this
shape has six vertices, we know that we’re going to need six blobs of modeling clay
too.
Now, how good do you think you are
at recognizing the edges of 3D shapes? Let’s answer a couple of questions
now where we have to put into practice what we’ve learned. And then afterwards, we’ll try a
challenge to really test us.
How many straight edges does this
shape have?
We can see a picture of a 3D or a
solid shape here. Can you think of any objects that
are the same as this shape? Looks the same as perhaps a block
of wood or maybe a long brick. The name of this shape is a
cuboid. We know that it’s a cuboid because
it has rectangular faces. It has four of these long
rectangular faces all the way around. And then, at each end is what looks
like it might be a square face. But we can just call them
rectangles because squares are a special type of rectangle anyway.
So, this shape, with rectangular
faces along the way around, is a cuboid. But although it’s helpful for us to
think about the faces of this shape, the question doesn’t ask us about its
faces. We need to say how many edges this
shape has. Do you remember what the edge of a
3D shape is? An edge of a 3D shape is the place
where two of its faces meet. It’s where the faces touch. So, if we pick two of the faces on
this particular cuboid, we’ve got this long rectangular face here and the square
face on the end.
Can you see the place where these
two faces meet? It’s along here. This is one of the edges of the
cuboid. If you imagine this cuboid is a
long cardboard box and you open it out and flatten it, we’d be able to see this
edge. It would be one of the folds. It’s where two faces meet. Did you notice this edge was one of
the black lines that makes up our picture? But unfortunately, because this is
a picture of a solid shape, we can’t see all of the edges. Some of them are hidden around the
back. Let’s try and visualize what our
shape looks like around the back. And we’ll use dotted lines to draw
in the extra edges.
Well, from what we know about
cuboids, the face on the bottom of this shape is exactly the same as the face on the
top. It’s going to be another
rectangle. In a way, this cuboid doesn’t
really have a top and a bottom because all we’d have to do is turn it upside down;
it’d look exactly the same. So, let’s draw in our missing sides
of this rectangle on the bottom of the shape, one at the side and one along the
back. And the sides of our rectangular
face become the edges of this 3D shape.
We’ve got one more edge that’s
missing. Can you spot where it belongs? It’s round the back on the left
here. And it shows us that the end of our
cuboid, there’s a square face. Can you see now that drawing in
these dotted lines really helps us to visualize the shape? We don’t need to imagine what it
looks like around the back; we can see.
Now that we’ve drawn in all of the
edges, let’s count them. There are four straight edges that
go all the way around this square face on the right. Then, there are another four edges
around the opposite end of the cuboid. And then, finally, there are four
more much longer edges that run along the length of the cuboid. So, that’s three groups of
four. We know that three times four
equals 12. So, we can say that the number of
edges that this shape has is 12.
How many edges does the pyramid
have?
We know this picture shows a
pyramid. And it’s not just because we’re
told so in the question. We know it because we know what
makes up a pyramid. This particular type of pyramid has
a square face as its base and then four triangular faces that all meet at a point or
a vertex right at the top. Now, our question asks us, how many
edges does the pyramid have? It doesn’t mention faces at
all. So, what have the faces of this
pyramid got to do with its edges? Well, we know that an edge of a 3D
shape is the place where two faces meet. It’s where they touch, where they
connect up with one another. And so, knowing what the faces of
this pyramid are like can really help us work out how many edges it has.
Remember, we started off by saying
that the face at the base of this pyramid is a square. That’s why on this picture we can
count one, two, three, four edges around the base. And because we know that the faces
around a pyramid are all triangles, they all go up to that point at the top. We know from each of the vertices
of this square base, we’re going to have one more edge. And four vertices means one, two,
three, four more edges. And four plus another four equals
eight. We know that the edges of a 3D
shape are those places where two faces meet. And by counting them, we found that
the number of edges that this pyramid has is eight.
Now, we did say we were going to
end the video with a fun challenge for you to try. You might like to pause the video
to have a think about this question or maybe even try building the shape
yourself. And the challenge is this. If you have six straws and four
blobs of modeling clay, which 3D shape can you build? And because we know what these
objects represent when we build a skeleton shape, we could’ve just asked which 3D
shape has four vertices and six edges. But perhaps that wouldn’t have been
as interesting as doing it this way.
Can you think what this shape might
look like? Here’s a clue. This is what the base of the shape
looks like. Can you think what to do with your
last three straws and one blob of modeling clay? This is the shape, isn’t it? It’s another kind of pyramid,
slightly different to the one we saw in the last question because the base of this
particular pyramid is a triangle not a square. So, interestingly, not all pyramids
have eight edges. Some pyramids have six edges. Why don’t you try making your own
3D shapes out of straws and modeling clay or cocktail sticks and marshmallows? Remember, each straw or each
cocktail stick that you use is another edge for your 3D shape.
So, what have we learned in this
video? We’ve learned how to recognize and
count the edges of 3D shapes. We’ve also learned ways to build 3D
shapes and used this to help us learn about their edges.
