Elements of a CONE

In this lesson that we bring you today from a Teacher we are going to talk about the elements of a cone, so we will previously explain what a cone is to later see its elements. This lesson is essential for the more advanced study of geometry and, therefore, of mathematics. In the end, we will propose a exercise and its respective solution.

Index

1. What is a cone and types
2. What are the elements of a cone
3. Exercise on the cones
4. Solution

A cone is a geometric figure in three dimensions which is created by wrapping a triangle around one of its sides. In this way, the cones have a circular base. This geometric body is considered a body of revolution.

types of cones

Something important to mention is that the cones can be of different types, as we will see below:

1. straight cone, known as cone of revolution, which is one in which the curved surface is conic of revolution, which means something like the height is perpendicular to the base.
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2. Oblique cone with elliptical base, which is the one in which the height is not perpendicular and, therefore, does not pass through the center of the base, in addition to having an ellipse-shaped base. If the lateral face is a conical surface of revolution, the cross section will be a circle.
3. Oblique cone with circular base, which is the one in which the height does not pass through the center of the base either, as in the previous one.

We can find this geometric figure in our daily life more than we can think. For example, we can think of the cookie in an ice cream cone, a road safety cone or some bar glasses. We can also think of a diabolo, which is two cones joined by their vertices.

Here is a review of the main elements of a cone:

• a shaped base circular.
• A directive, which is the perimeter of the circular base of the cone and is a plane curve (a circle if it is a circular cone or an ellipse if it is an elliptical cone).
• A vertex, which is what is colloquially known as the upper peak.
• The generatrix, not to be confused with height. The generatrix is ​​what the side of the cone measures, from any end of the base to the vertex.
• The height, which is the imaginary line that goes from the central point of the circular base to the vertex. It should not be confused with the generatrix.
• The opening, which is the largest angle between two generating lines.

In this other lesson we tell you how to get the area and volume of a cone.

We leave you below some activities so that you can put into practice what has been explained in today's lesson about the elements of a cone:

1. State whether the following sentences are true or false, justifying the corresponding answer:

• A cone is a two-dimensional geometric figure.
• Cones are created by rolling a rectangle from a circular base.
• The generatrix is ​​one of the elements of the cones.

2. Find more examples of cones in everyday life.

Now let's check that you have correctly carried out the activities proposed in the previous section, to see if you have managed to understand the lesson:

1. State whether the following sentences are true or false, justifying the corresponding answer:

• A cone is a two-dimensional geometric figure: false, since cones are figures in three dimensions.
• Cones are created by rolling a rectangle from a circular base: false, since what is rolled on the circular base is a triangle, not a rectangle.
• The generator is one of the elements of the cones: true, among others, the generator is one of the elements of the cones.

2. Find more examples of cones in everyday life:

Open response, any cone-shaped object, at the discretion of the student.

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