Three-dimensional objects can be represented with the side elevation, front elevation, and top elevation (called plan) clearly indicated on a two-dimensional surface. We can then ask about the view from each of these elevations.

Consider this solid formed from cubes:

3 dimensional object made of blocks with side, plan, and front elevations labelled. Ask your teacher for more information.

What is the front view?

3 dimensional object made of blocks with front elevation highlighted. Ask your teacher for more information.

We can colour the sides of the cubes that are facing the front to make an image like this.

A front view of the three-dimensional object. Ask your teacher for more information.

We can now piece together the front view by joining the highlighted faces together.

3 dimensional object made of blocks with plan elevation highlighted. Ask your teacher for more information.

We can do the same from above to get the plan view.

A plan view of the three-dimensional object. Ask your teacher for more information.

Looking up and over from the side, we can tell that this is the plan view.

3 dimensional object made of blocks with side elevation highlighted. Ask your teacher for more information.

When thinking about the side view, we can again use the same trick.

However, this time there is a highlighted face that would be hidden from the side that we don't include.

A side view of the three-dimensional object. Ask your teacher for more information.

Once we have identified this hidden side, we can draw the side view properly.

Examples

Example 1

Consider this solid formed from cubes:

3 dimensional object with side, plan, and front elevation labelled. Ask your teacher for more information.

Which of the following diagrams represents the plan view?

4 squares in a backwards L shape. Ask your teacher for more information.

5 squares making a shape. Ask your teacher for more information.

4 squares in an L shape. Ask your teacher for more information.

Worked Solution

Create a strategy

Try imagining the tops of each cube as a different colour:

A solid formed from cubes highlighting the plan view. Ask your teacher for more information.

Apply the idea

Joining the highlighted faces together, the diagram which represents the plan view is given by:

The correct answer is Option B.

Which of the following diagrams represents the side view?

Worked Solution

Create a strategy

Try imagining the sides of each cube as a different colour:

A solid formed from cubes highlighting the side view. Ask your teacher for more information.

Apply the idea

Joining the highlighted sides of each cube, the diagram which represents the side view is given by:

A diagram representing the side view of the solid formed from cubes. Ask your teacher for more information.

The correct answer is Option B.

Which of the following diagrams represents the front view?

4 squares making a shape. Ask your teacher for more information.

4 squares in backwards L shape. Ask your teacher for more information.

Worked Solution

Create a strategy

Try imagining the fronts of each cube as a different colour:

A solid formed from cubes highlighting the front view. Ask your teacher for more information.

Apply the idea

Joining the highlighted fronts of each cube, the diagram which represents the front view is given by:

A diagram representing the front view of the solid formed from cubes. Ask your teacher for more information.

The correct answer is Option D.

Idea summary

Three-dimensional objects can be represented with the side elevation, front elevation, and top elevation (called plan):

3 dimensional object made of blocks with side, plan, and front elevation labelled. Ask your teacher for more information.

Views of 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.

Hexagonal prism with 3 rectangular sides highlighted.

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

A rectangle divided vertically into 3 smaller rectangles. The middle rectangle is wider than the other two.

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.

An eye looking to the sloped front view of a hexagonal prism. Ask your teacher for more information.

This is because the sloped sides aren't as wide when viewed directly from the front. As is shown in this diagram , 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.

A cylinder with its 3D view and its plan, side, and front views indicated. The front view is shown as a rectangle.

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

An eye looking to the curved front view of a cylinder.

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

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

Triangular prism with its plan, side, and front views labelled.

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.