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16.01 Nets of solids

Lesson

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.

Exploration

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

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The net of a triangular prism is made up of three rectangles and two triangles.

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:

Table of prisms containing triangular, square, rectangular, pentagonal, hexagonal, and octagonal 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:

Table of pyramids containing triangular, square, rectangular, pentagonal, hexagonal, and octagonal 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:

Image of rectangular prism.
A
This image shows a net of a solid made of 4 triangles and 1 rectangle. Ask your teacher for more information.
B
This image shows a net of a solid made of 6 rectangles. Ask your teacher for more information.
C
This image shows a net of a solid made of 4 triangles and 1 rectangle. Ask your teacher for more information.
D
This image shows a net of a solid made of 6 rectangles. Ask your teacher for more information.
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.

Example 2

Choose the shape that has the following net:

This image shows a net of a solid made of 4 triangles and 1 square. Ask your teacher for more information.
A
Image of a rectangular pyramid.
B
Image of a square pyramid.
C
Image of a rectangular prism.
D
Image of a cube.
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.

Idea summary

Prisms have rectangular sides, and the shape on the top and the base is the same. Any cross-section taken parallel to the base is always the same.

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

Outcomes

MA4-14MG

uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume

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