Calculate the Surface Area of a Cylinder

By Mark Ryan

A cylinder has two congruent bases, which makes it easy to calculate its surface area: you simply find the area of one base and double that value; then you add the cylinder’s lateral area (or lateral “rectangle”).

geometry-cylinder
A cylinder with its bases and lateral “rectangle.”

As shown here, the lateral area of a cylinder is the area of the sides of the cylinder—namely, the area of everything but the cylinder’s bases. Think of the lateral area of a cylinder as one rectangular paper towel that rolls exactly once around a paper towel roll. The base of this rectangle (you know, the part of the towel that wraps around the bottom of the roll) is the same as the circumference of the cylinder’s base. And the height of the paper towel is the same as the height of the cylinder.

To find the surface area of a cylinder, you can use the following formula:

geometry-sacylinder

Now let’s take a look at this formula in action:

Given a cylinder as shown with a radius of 4, a height of 7, find the cylinder’s surface area.

geometry-radius-revised

Remember that this “rectangle” is rolled around the cylinder and that the “rectangle’s” base is the circumference of the cylinder’s circular base. Using the surface area formula, you fill in the equation as follows:

geometry-sa-finished