3D shapes have faces, vertices & edges and can be viewed from different points. All 3D shapes have 3 dimensions - length, width and height. 3D shapes unlike 2D shapes have a volume as there is space inside of them.

Types of 3D shapes:




Triangular prism



Hexagonal prism



Plus many more...

Today we're going to be looking at the properties of some common three dimensional shapes, common sense, the times of the ancient Greeks and ancient Egyptians. This shape up here in particular is a square based pyramid, pyramid, which is exactly what the great pyramid of Giza is. So these shapes are very common. Of course, most skyscrapers are essentially a cuboid stood on end. But we're going to be looking at three properties in particular of these three dimensional shapes that you do need to know for your exams and you need to be able to tell apart.

So the three properties are faces, edges and vertices. So what are they? Well, a face is the two dimensional surface that faces you. So in this cube, this face is a square. In this triangular prism, the face that faces me is this triangle.

This face on the right hand side is a rectangle. So it's the ones that you could reach out with the palm of your hand and touch. An edge is like this one up here. It's like running your finger along the edge of a knife. Don't do that.

It is the straight length, the line that is the end that joins faces. So we were saying before, this is a triangle and this is a rectangle. Well joining two faces are edges, so each face is joined by an edge. And lastly, vertices. Those are the points, the corners, the one dimensional points that join the edges.

Way of remembering that is in the word vertices. The V Invertex looks like a little corner, a little point, which is exactly what it is, it's a vertex, a point. So we're going to count these up and in particular pay close attention to the cone, the sphere and the cylinder which will come to last because the curve nature of those often confuses people. So we'll start with the linear shapes, the rectangular pyramid, just like Giza. Well what are the number of faces?

Well if we count them we have the one that faces us, the one at the back, the one at the left, the one at the right, there's four and then underneath what it's resting on, there's five. So there's five faces, edges is bottom and vertices 1234 and five at the point right at the top, five, eight, five. Next we'll do the cube number of faces. Well it's the same as the number of sides and a dice. It's six, one at the front, one at the back, one at the top, one at the bottom, one at the left, one at the right, six faces, edges.

Be careful that you don't miss any that are behind in the shape 1234 coming out the page front, 910, 1112 on the back, twelve edges and the number of vertices, 1234 at the front, 5678 back, eight vertices in total. And the triangular prism will start with the number of faces. Again, we've got the front and the back. There's two. This one gets a little bit trickier to visualise.

You've got this rectangle on the right here, there's three. You've also got that rectangle on the left, the back there. There's four. And you've got the base that it rests on. So there's five faces.

Number of edges. Well, we have the obvious one, two, three at the front from the triangle and the one, two, three at the back there's six. You've also got the one, two, three going into the page, making a grand total of nine edges and the number of vertices, 12345, six. There we have five, nine and six. Now to the ones that have some curved surfaces.

Here's where it gets a little bit trickier. If we look at this cone here, the number of faces. We've got this obvious one on the bottom, but this curved edge around the whole cone, like an ice cream cone, that is just one face. It curves around. So the number of faces is just two.

Edges can also be confusing here. What are my edges? Many people might think there's this curved edge at the bottom that you could run your finger long, which is true, that's one edge. And then they might look at the shape and say, well, this is another edge there and that's another edge on the right there. That's not true.

That's just a trick of perspective. If you ran your hand around there, it would be smooth. There's no edges there at all. The only one edge is that one that you could run your finger along and it would feel sharp along the bottom. That's one edge.

And vertices, that's that point right at the top. Two, one, one. What about the cylinder? Well, we have one curved edge faces first. We have that one curved face all the way around.

We have the face at the top and the face at the bottom. So we have three faces. We have in terms of edges, this curved edge at the top, this curved edge that I could run my finger along and it would feel sharp at the bottom. And these two at the sides are not edges, they just look like edges. If you imagine moving your hand around a three dimensional cylinder like a tin of beans, it's smooth all the way around.

So we have two edges, one at the top and one at the bottom. And what about the number of vertices? Well, do you see any points? No. That's because there aren't any.

No corners, no vertices. And finally the sphere. The strangest one number of faces and the sphere. Well, if imagine you run your hand across a perfectly spherical ball. Do you feel any edges?

No, you do not. There is only one continuous face. Of course there are no edges, so the number of edges is zero. And are there any points on the sphere? No, not at all.

One face, no edges and no vertices. Okay, now we're going to move on to just some exam questions of this and see how they are applied.

So here is an exam question. We have to given this solid find the number of faces and find the number of vertices. So let's approach this carefully. In an exam situation, you're given these dashed lines at the back. That's your ability to see behind the shape as well as see the front.

It's often a good idea to use your pen and then mark the faces so that you know right in the middle, so that you know that you've not missed any. So this face at the front will put a nice big mark there. That's one at the top, two, one at the right, three. Are there any missing? Yes, there are.

There's this shape here, this rectangle, which makes up the base at the very bottom. That's also one that we missed. And then we've got this rectangle on the left. There dot in the middle of that, there's other ones. So what do we have in total?

12345. And are there any we've missed? Yes, there are. There's this trapezium shape right at the back. Put a dot there.

So in grand total, we have six faces for this shape. Again, that little hint. Putting the dot right in the middle can also be very useful. And because it's in the middle, you're not going to confuse it with any of the other dots. Now, what about the number of vertices?

A bit easier. This one. Just check all the points where the edges meet, do it in a different colour. We have 123-4567 and eight. That's eight vertices in total.

So that would be your marks for that. Question. One for you guys in the comments section, what is the name of this three dimensional shape? I'll give you a hint. It is not a trapezium or a 3D trapezium.

There is a special mathematical name for it. Does anyone know? If you do not know, put it in the comments section. If you'd like to get in touch with myself, my name is Adam, a tutor for Sherpa or any other sherpa tutor, I'm sure they can let you know the answer as well.

Have a good day, guys. Enjoy. Bye.

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Adam S

A highly experienced GCSE tutor, Adam is straight to the point, embodying the “I do, we do, you do” philosophy. He lives for the chance to hear about how his tutees have improved.

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