# Right Cone: Surface Area

How to find the surface area of a right cone: definition, formula, 1 example, and its solution.

## Cone

### Definition

A cone is a 3D figure

that has a vertex, a circle base,

and a lateral face.

## Right Cone

### Definition

A right cone is a cone

whose vertex and the center of the base circle

are the endpoints of the height of the cone.

## Formula

### Formula

A = πr^{2} + πrh_{s}

A: Surface area of a right cone

r: Radius of the base circle

h_{s}: Slant height (= Height of the lateral face)

## Example

### Example

### Solution

See this right triangle.

The radius of the base is 3.

The height is 4.

Set the slant height h_{s}.

Then the sides of the triangle are (3, 4, h_{s}).

So this right triangle is

a (3, 4, 5) right triangle.

Pythagorean Triple

So the slant height, h_{s}, is 5.

r = 3

h_{s} = 5

Then the surface area, A,

is equal to,

the base area, π⋅3^{2}

plus,

the lateral area, π⋅3⋅5.

So A = π⋅3^{2} + π⋅3⋅5.

π⋅3^{2} = 9π

+π⋅3⋅5 = +15π

9 + 15 = 24

So the surface area of the right cone is

24π.