Properties of Cylinders
Rule

Surface Area of a Cylinder

Consider a cylinder of height and radius
Cylinder with a radius of r and height of h

The surface area of this cylinder is given by the following formula.

Proof

The cylinder's surface area can be seen as three separate parts that are top, bottom, and side. The area of the side has the shape of a rectangle of width The top and the bottom are circles of radius

Cylinder with expanded surface areas
Since the top and the bottom are congruent circles, they have the same area.
To find the area of the rectangle, its length must be found first. The length of the rectangle that forms the lateral part of the cylinder is the circumference of the base, which is
Cylinder with expanded surface areas
Therefore, the area of the rectangle is the product of and
The surface area of the cylinder is the sum of the areas of the rectangle and the circles.

Exercises