Right Cylinder: Surface Area

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

Cylinder

Definition

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

Definition

A right cylinder is a cylinder
whose centers of the bases
are the endpoints of the height.

Formula

Formula

A = 2⋅πr2 + 2πr⋅h

A: Surface area of a cylinder
r: Radius of the base circle
h: Height

2πr2 are the two base areas (= circle).

Circle: Area

2πr⋅h is the lateral area.
(2πr is the circumference of the base circle.)

Circle: Circumference

Example

Example

Solution

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⋅42

times,
the lateral area,
2π⋅4 times 9.

So A = 2⋅π⋅42 + 2π⋅4⋅9.

2⋅π = 2π
42 = 16

4⋅9 = 36

2π⋅16 = 32π

+2π⋅36 = +72π

32 + 72 = 104

So the surface area of the right cylinder is
104π.