One way we can tell different solids apart is by comparing what these solids look like from different views. By being seeing what a solid will look like from a particular angle, we can recognise different solid shapes in our world by connecting them to how they look from different views.

Ideas

Different views of solids

Different views of solids

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.

Rectangular prism showing front, side, and plan views.

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.

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.

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.

An eye looking to the plan view of a triangular prism. Ask your teacher for more information.

Looking at these two sloped faces from directly above, like this ...

A rectangle divided horizontally into 2 equal rectangles.

We find that the top view of this triangular prism looks like this.

The fact that we can see two faces from the top view is shown by the line dividing the view into two rectangular faces.

Examples

Example 1

Consider the different views of this trapeziumal prism.

A trapeziumal prism with its plan, front, and side views labelled.

What is the front view?

A horizontal rectangle divided into 3 rectangles where middle rectangle is wider than the other two.

Worked Solution

Create a strategy

Think of the 2D shape that we would see if we looked directly at the front of the given shape.

Apply the idea

We can see a trapezium in front, so the answer is option A.

What is the side view?

Worked Solution

Create a strategy

Think of the 2D shape that we would see if we looked directly at the side of the given shape.

Apply the idea

We can see a vertical rectangle to the side, so the answer is option B.

What is the top view?

Worked Solution

Create a strategy

Think of the 2D shape that we would see if we looked directly at the top of the given shape.

Apply the idea

We would see a horizontal rectangle for the top two smaller rectangles for each side, forming one horizontal rectangle. So the answer is option C.

Example 2

Choose the solid that would have this front view:

Worked Solution

Create a strategy

Look at the shape at the front of each solid.

Apply the idea

We need choose the solid that has rectangle at its front.

The rectangular prism has rectangle at its front, so the answer is optiion D.

Idea summary

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

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

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.

2D views can't show that one end is further away than the other or that one side of a solid is curved when we look directly at it.

9.09 Views of solids

Introduction

Ideas

Different views of solids

Examples

Example 1

Example 2

What is Mathspace

About Mathspace