Visualising Prisms

We have already seen how 3D shapes can be unfolded to create Nets.  The questions that follow will give you practice at matching nets to their solids.  

When I have to match a solid to its net I look at the parts I'm given.

Prisms

If you can identify two identical polygon pieces which could be two opposite ends of a solid, and also identify pieces that would wrap around it, you might have a prism.

 Like this hexagonal prism.    

Points to remember

If you think you have a prism, make sure 

• the ends are identical pieces
• there are the appropriate number of faces to wrap the base
• the end pieces are positioned appropriately

Pyramid

If you can identify a polygonal base and pieces that can fold up from the base to meet at an apex, you might have a pyramid.  

     Like this square based pyramid.

Cone

The nets of cones are pretty unique, with a circular segment and circular base.

Viewing Faces

Another thing we can do with 3D shapes is draw or identify the different views of the shape depending on where we view the solid from.  We can view (or look at) objects from different angles, and we call these VIEWS or ELEVATIONS.  

• FRONT view or elevation is what you see if you are directly in front of it
• SIDE view or elevation, is what you see if you are directly to one side. You can have a left or right view of a shape or object.
• TOP view or elevation, is what you see if you are over the top or above it. 

Example

By imagining ourself looking directly in the direction of the arrows, we can come up with the following views.

 

Worked Examples

Question 1

Consider the following diagram of a solid.

a) What is the name of the solid?

b) Which of the following is a new of the given solid?

 

Question 2

Consider the following diagram of a solid.

a) Which of the following diagrams represents the top view of the given solid?

b) Which of the following diagrams represents the front view of the given solid?

c) Which of the following diagrams represents the side view of the given solid?  

 

Question 3

Which of the objects below have the following cross-section?