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Geometry - Nets of Solids




 
In these lessons, we will learn:
  • What is meant by the net of a solid?
  • Nets of the following solids: cube, rectangular prism or cuboid, triangular prisms, pyramids, cylinders and cones.
  • How to use nets to find surface area?


Nets of a Solid


A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.

Below are the steps to determine whether a net forms a solid:

1. Make sure that the solid and the net have the same number of faces and that the shapes of the faces of the solid match the shapes of the corresponding faces in the net.

2. Visualize how the net is to be folded to form the solid and make sure that all the sides fit together properly.

Nets are helpful when we need to find the surface area of the solids. Scroll down the page to see how the nets fold to form the various shapes.

Nets of a Cube and a Cuboid

A cube is a three-dimensional figure with six equal square faces.

cube

There are altogether 11 possible nets for a cube as shown in the following figures.

all possible nets of a cube



A rectangular prism or cuboid is formed by folding a net as shown:

net of a cuboid




This video shows how to draw a net of a rectangular prism or cuboid.
This video shows how to create different nets of a cube and rectangular prism.


 

Nets of Prisms, Pyramids, Cylinders and Cones

Here are some examples of nets of solids: Prism, Pyramid, Cylinder and Cone

net of triangular and rectangular prism

net of cylinder and cone

This video shows the net of a cuboid, triangular prism, cylinder, and square pyramid.
Learn about faces, edges and vertices.


This video shows how to identify the 3-dimensional shapes made by the nets - cube, rectangular prism or cuboid, triangular prism, and pyramid.
In this video, we analyze the net of a cylinder to determine volume and surface area.
The diagram below shows a net for a cylinder.
a. Suppose the net is assembled. Find the volume of the cylinder.
b. Find the surface area of the cylinder.


 
This video shows how to use nets and 3-dimensional figures to find surface area of cubes and prisms.

For animations to explore how 3D shapes unfold into nets and how nets fold to form geometric solids, see:


You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.


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