### 3D Shapes

3D shapes have depth.

Here are some to learn:

Cube

Cuboid

Sphere

Cylinder

Cone

Prism

Pyramid

Tetrahedron

### Plane Symmetry

**Plane symmetry** is like a line of symmetry in 2D shapes.

Instead of being **reflected** across a line, the 3D shape has plane symmetry if it can be reflected **across a plane**.

A plane is just a **flat surface**.

Here is a **prism** with a plane of symmetry drawn on to it:

Think of the plane of symmetry like **a mirror**, the two parts of the shape on either side of it are **identical**.

This prism actually has 3 more **planes of symmetry** that aren’t shown, can you see where they would be?

### Faces, Edges and Vertices

Here are some **important words** to learn that we use when talking about 3D shapes:

- A vertex is the
**corner**of a shape, it is the**point**where two or more edges meet. - An edge is the
**line**around a face of the shape. - A face is the
**surface**of the shape**between the edges**.

### Shape Nets

If you folded out all the faces of a shape, a bit like peeling an orange, you would have a shape net.

A shape net is a **flat diagram** that would fold back together **along the edges** to make a 3D shape.

You have to **use your imagination** a bit when thinking about shape nets because you must try to see how a diagram could fold together to make a 3D shape.

Here is a shape net for a **cube**:

Can you imagine how it would **fold together**? Here it is part way through being being folded up:

And here it is complete:

This cube doesn’t just have this one shape net, there are **many ways** it could be unfolded and put back together. This is just one example.

Here is a shape net for a **pyramid**:

Here it is partly folded together:

And here’s the final pyramid:

### Volume

**Volume** is the amount of **space inside** a 3D shape.

It is similar to area for 2D shapes, but volume has 3 dimensions. It is like area but **extends back** through a 3D shape.

Volume is measured in **units³**

For example cm³ or m³

The volume of a **cube** or **cuboid** is worked out by using:

width x height x depth

You work out the area of a face (width x height) then multiply this by the depth to **fill the whole shape**.

Here is a **cuboid** made up of **small cubes**:

Each of the **small cubes** inside the cuboid has a width, height and depth of **1 cm**.

The **volume** of each small cube is therefore:

1 x 1 x 1 = 1 cm³

The cuboid is made up of **20** of these **small cubes**. You can see 10 of them clearly in the top half, and the bottom half will be identical.

So the volume of the cuboid is **20 cm³**

Let’s think about this in more detail, because you won’t always be give shapes made up of small cubes.

The **width** of the square face at the front of the cuboid is 2 cm. It is also 2 cm in **height**. The cuboid has a **depth** of 5 cm.

The area of the front face is:

width x height

2 x 2 = 4cm²

The volume of the cuboid is:

Area of the face x depth

4 x 5 = **20 cm³**

Or, ignoring the area and putting it all together at once, the volume is:

width x height x depth

2 x 2 x 5 = **20 cm³**