2. Geometry and Scale Drawings

2.02 Properties of 2D shapes

2.025 Properties of 3D solids

2.03 Nets and 3D shapes

Lesson

Worksheet

Practice

2.04 Interpret plans, elevations and architectural drawings

Investigation: Photogrammetry

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Australia WA

Year 12

2.03 Nets and 3D shapes

Lesson

Worksheet

Practice

Lesson

Three-dimensional objects are represented on two-dimensional surfaces all the time. Screens, whiteboards, paper, and other flat surfaces can create the illusion of depth when displaying a picture of something.

There are a few tricks we can use to think about three-dimensional objects represented on a flat surface.

Nets

We can never see every part of a three-dimensional object at once - there is always part of it that is behind the view we are looking at. To better think about a solid object we sometimes represent it with its net. Each face of the solid is laid flat on the same surface, breaking it along the edges and folding it out. This way we can think about folding it back up along its edges to recover the original shape.

Here is a triangular prism. Move the slider to see its net unfold:

Created with Geogebra

Practice questions

Question 1

Choose the net that folds to give the shape below:

A
B
C
D

Question 2

Choose the shape that has the following net:

A
B
C
D

Different views of prisms

When looking at a prism, we can look at the prism from a 3D view or from one of the 2D views.

A 3D view of the prism shows us what the whole solid looks like from an angle. From this perspective, we can see the faces that will be visible when looked at directly from one of the 2D views.

The 2D views show what the solid looks like when viewed directly from the front, side or top.

In the 3D view of this rectangular prism we can see the sides that will be visible in the 2D views. In each 2D view we look at the rectangular prism directly from either the front, side or top.


3D view	Front View	Side View	Plan View

As we can see from the images, the front, side and top views are all 2D shapes that match the faces of the prism visible from each view when looked at directly.

Did you know?

The plan view is another name for the top view and is used in architecture when referring to the plan of a building, which is how the building looks when viewed from directly above.

An elevation can be used to describe the front, back or side views. Elevations are used in architecture to show how the building looks when viewed from the front, back or sides.

Viewing sloped and curved sides

Since the 2D views of a solid only show what the solid looks like directly from one angle, these views cannot show depth like how a 3D view can.

For example, if we look at this hexagonal prism from the front, we will be able to see these three faces.

The faces visible from the front view of the hexagonal prism

However, two of these faces are sloped and will appear thinner in the front view than they actually are. As a result, the front view will look like this:

The front view of the hexagonal prism

This is because the sloped sides aren't as wide when viewed directly from the front. As is shown in the diagram below, the distance between the two ends of the sloped sides is closer together when viewed from the front because the 2D view doesn't show that one end is further away than the other.

Looking at sloped sides directly

For a similar reason, the side view of a cylinder will look like a rectangle:


3D view	Front View

Curved sides in 3D will always look flat in a 2D view.

Looking at curved sides directly

Viewing other sides

A 2D view might also show a side that we can't see from the 3D view.

When looking at a triangular prism from the 3D view, we notice that we can only see two of the five faces. The bottom and back faces of the prism won't show up on any of our 2D views but the last hidden face will be visible from the top view.