# Surface Area of a Right Cone

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

## Cone

A cone is a 3D figure

that has

a [vertex], a [circle base],

and a [lateral face]

which is adjacent to the vertex and the base.

## Right Cone

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

*A* = *πr*^{2} + *πrh _{s}*

*A*: Surface area of a right cone

*r*: Radius of the base

*h*: Slant height of the right cone

_{s}(= Distance between

the vertex and the rim of the base circle)

*πr*

^{2}: Base area

*πrh*: Lateral area

_{s}## Example

The radius of the base circle is 3.

So *r* = 3.

See this right triangle.

Starting from the shortest side,

the sides are (3, 4, *h _{s}*).

So this is a (3, 4, 5) right triangle.

Pythagorean triples

So

*h*= 5.

_{s}*r* = 3*h _{s}* = 5

So

*A*=

*π*⋅3

^{2}+

*π*⋅3⋅5.

3^{2} = 9

3⋅5 = 15

9 + 15 = 24

So *A* = 24*π*.