3D shapes have depth.
Here are some to learn:
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.
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 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