The net of a cone is a 2D shape or a 2D pattern that can be folded to form a 3D shape, in this case, a cone. The net of a cone consists of a circular base and a curved surface that forms the lateral surface of the cone.

Here, we will look at the diagrams of the net of a cone. In addition, we will learn about some important characteristics of these nets.

GEOMETRY
net of a cone when l is greater than 2r

Relevant for

Learning about the geometric net of a cone with diagrams.

See nets

GEOMETRY
net of a cone when l is greater than 2r

Relevant for

Learning about the geometric net of a cone with diagrams.

See nets

Characteristics of the net of a cone

A cone is a three-dimensional figure that has a circular base and a lateral surface with a pointed top. This means that the geometric net must include a circular base and a curved surface. In the following animation, we can see how the geometric net of a cone is formed.

net of a cone animation

Depending on the relationship between the radius and the height of the cone, we can obtain three variations of this net, which are shown in the following diagram.

three cases of net of a cone

To determine which of the three nets corresponds to a given cone, we have to compare the length of the radius with the length of the slant height of the cone. Then, we have the following:

1. If the slant height, represented with l, has a length equal to 2r (equivalent to the diameter), the cone will form the following geometric net:

net of a cone when l is equal to 2r

2. If the slant height has a length less than 2r, the cone will form the following geometric net:

net of a cone when l is less than 2r

3. If the slant height has a length greater than 2r, the cone will form the following geometric net:

net of a cone when l is greater than 2r

Characteristics of the net of a cone

Geometric nets have the main characteristic of being two-dimensional figures that can be folded to form a three-dimensional figure. This means that when we fold a 2D net of a cone, we will form a cone, which is a 3D shape.

The geometric net of a cone consists of the following parts:

  • Base: This is the circular base of the cone, which has a radius of r.
  • Lateral surface: The lateral surface is a circular sector. That is, it is a part of a circle that has a radius of l, the slant height of the cone.

The base of the cone remains in the same position in the geometric net. That is, the base is still a circle with radius r.

The lateral surface of the cone is expanded to form a sector of a circle. The slant height or lateral side of the cone represented by l becomes the radius of the formed sector.

The length of the arc of the formed sector corresponds to the circumference of the base, that is, it is equal to 2πr.


See also

Interested in learning more about nets of 3D figures? Take a look at these pages:

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