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# Cones- Types, Properties, and Formulae

There are a number of geometrical shapes present in the vast topic of geometry and in the subject of mathematics. The different geometrical shapes are differentiated on the basis of different factors such as their different properties. These properties are different for each of the different shapes. Let us try to understand with the help of an example. Suppose we have the volume of cone, then it has a fixed definite formula which is different from any other property of the cone or any other formula of any other such geometrical shape.

# Cones- Types, Properties, and Formulae

A cone is a 3d geometrical shape which is a closed figure. If the figure is examined closely then we see it consists of two shapes namely a circle and a triangle. The base is circular in shape and the top part is triangular in shape. The length of the line that stands vertically between the vertex of the triangle to the circular base is known as the height of the cone and half of the diameter of the circular base is known as the radius. These two things are crucial in determining the slant height of the cone which is the square root of the individual sum of squares of the height and radius of the cone. Mathematical representation can be witnessed below:

We have, l= √(h2+r2)

Where, l= slant height, r= radius of the cone and h= height of the cone.

### There are various types of cones. Let us have a look at some of them which are mentioned below:

• Right circular: This is the usual type which is seen at most of the places. In the right circular the vertex is located right perpendicular to the base. This means if a line is drawn from vertex to the circular base then the angle subtended by that line on the base or to say the angle between the line and the circular base will be exactly equal to 90 degrees. Due to the presence of this right angle the word “right” has been added to the name of this kind of cone.
• Oblique: This is a not so common kind of cone which is generally known or taught to the students. Here the difference between both of these cones lies in the position of the vertex. In the right circular the vertex was perpendicular to the circular base of the cone. But  here the vertex is not exactly perpendicular to the base. The vertex here is tilted to the left or right direction by a bit, so this is where the main difference lies between both of these.

### Some properties of cones:

• There are no edges present.
• It only has 1 face which is the circular base.
• Properties such as volume, surface area etc. remain the same for both types of cone.

### Formulas of cones:

• Volume = (πr2h)/3.
• Total surface area = πrl+πr2
• Surface area = πr2
• Lateral surface area = πrl.

Here, π is a constant which is equal to 22/7.

r = radius of the base.

h = height, that is the vertical separation between the vertex and base.

l = slant height.

#### Calculation of several properties:

The formulae which are listed above are used in calculation of the respective properties. These properties are immense in both the theoretical aspect and the practical as well. Real world application of these formulae can be witnessed in the field of engineering and architecture. The construction of several architectures such as houses, bridges etc. are the real world applications of these formulae apart from the usual classroom learning imparted to the students in schools and colleges.

For a detailed explanation visit the Cuemath website.

#### Conclusion:

Retrospection of the facts and details mentioned above regarding the different aspects of the geometrical shape fetches a number of unique insights to the table and enlightens us on the topic. We saw different types of cones, the formulae used for calculation of properties and the real life implantation of these.

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