16.01 Nets of solids

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.

There are many ways to unfold a net from a solid, and in this chapter we will investigate nets of prisms and pyramids.

Here are some prisms:

Prisms have rectangular sides, and the shape on the top and the base is the same. The name of this shape gives the prism its name. Any cross-section taken parallel to the base is always the same.

Here are some pyramids:

Pyramids have triangular sides, and the shape on the base gives the pyramid its name. Any cross-section taken parallel to the base is always the same shape, but is smaller in size than the base.

Examples

Example 1

Choose the net that folds to give the shape below:

A

B

C

D

Worked Solution

Create a strategy

Choose the net that has the same number of faces as the solid and can be folded up along its edges to make the solid.

Apply the idea

The answer is option D.

Watch question walkthrough

Example 2

Choose the shape that has the following net:

A

B

C

D

Worked Solution

Apply the idea

Since there is only one square and all the other sides are triangles, it must be a square pyramid.

The answer is option B.

Watch question walkthrough