# Right Cylinder: Surface Area

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

## Cylinder

A cylinder is a 3D figure

that has

a pair of circle bases

and a lateral face.

The bases are congruent and parallel.

## Right Cylinder

A right cylinder is a cylinder

whose centers of the bases

are the endpoints of the height.

## Formula

A = 2⋅πr^{2} + 2πr⋅h

A: Surface area of a cylinder

r: Radius of the base circle

h: Height

2πr^{2} are the two base areas (= circle).

Circle: Area

2πr⋅h is the lateral area.

(2πr is the circumference of the base circle.)

Circle: Circumference

## Exampler = 4, h = 9, A = ?

The radius of the base is 4.

So r = 4.

The height h is 9.

Then the surface area A

is equal to,

the two base areas, 2⋅π⋅4^{2}

times,

the lateral area,

2π⋅4 times 9.

So A = 2⋅π⋅4^{2} + 2π⋅4⋅9.

2⋅π = 2π

4^{2} = 16

4⋅9 = 36

2π⋅16 = 32π

+2π⋅36 = +72π

32 + 72 = 104

So the surface area of the right cylinder is

104π.