# Cone

The **cone** is a solid of revolution generated by a right triangle that rotates around one of its **legs**.

### Axis

The **axis** is the fixed leg about which the triangle turns.

### Base

The **base** is the circle that forms the other leg.

### Height

The **height** is the distance from the apex to the base.

### Slant Height

The **slant height** is the distance from any point on the circumference to the apex of the cone.

By the Pythagorean theorem, the **slant height** of the **cone** is equal to:

#### Unfold of a Cone

### Lateral Area of a Cone

### Surface Area of a Cone

### Volume of a Cone

#### Examples

For a party, Louis has made about 10 conical hats out of cardboard. How much cardboard was used in total if each cap has a radius of 15 cm and a slant height of 25 cm?

Calculate the lateral area, surface area and volume of a cone whose slant height is 13 cm and its base radius is 5 cm.

Calculate the lateral area, surface area and volume of a cone whose height is 4 cm and its base radius is 3 cm.