Surface Area of a Right Cylinder

Surface Area of a Right Cylinder

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

Cylinder

A cylinder is a 3D figure that has a pair of circle bases and a lateral face which is adjacent to both bases.

A cylinder is a 3D figure
that has
a pair of circle [bases] (brown)
and a [lateral face]
which is adjacent to both bases.

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.

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

So, just like a right prism,
the lateral face of a right cylinder is a rectangle
that is perpendicular to the bases.

Surface area of a right prism

Formula

A = 2*pi*r^2 + 2*pi*r*h. A: Surface area of a right cylinder, r: Radius of the base, h: Height of the right cylinder

A = 2⋅πr2 + 2πrh

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

2⋅πr2: Sum of the base areas
2πrh: Lateral area

Example

Find the surface area of the given right cylinder. r = 4, h = 9.

r = 4
h = 9

So A = 2⋅π⋅42 + 2π⋅4⋅9.

42 = 16
4⋅9 = 36

2⋅16 = 32
2⋅36 = 72

32 + 72 = 104

So A = 104π.