# Definition:Cone

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## Definition

A **cone** is a three-dimensional geometric figure which consists of the set of all straight lines joining the boundary of a plane figure $PQR$ to a point $A$ not in the same plane of $PQR$:

### Base

The plane figure $PQR$ is called the **base** of the cone.

### Apex

In the above diagram, the point $A$ is known as the **apex** of the cone.

### Height

Let a perpendicular $AE$ be dropped from the apex of a cone to the plane containing its base.

The length $h$ of the line $AC$ is the **height** of the cone.

## Right Circular Cone

A **right circular cone** is a cone:

- whose base is a circle
- in which there is a line perpendicular to the base through its center which passes through the apex of the cone:
- which is made by having a right-angled triangle turning along one of the sides that form the right angle.

In the words of Euclid:

*When, one side of those about the right angle in a right-angled triangle remaining fixed, the triangle is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a***cone**.

And, if the straight line which remains fixed be equal to the remaining side about the right angle which is carried round, the cone will be**right-angled**; if less,**obtuse-angled**; and if greater,**acute-angled**.

(*The Elements*: Book $\text{XI}$: Definition $18$)

## Double Napped Cone

A **double napped cone** is a cone where the lines joining the apex to the circumference of the base extend indefinitely in either dimension: