Finding the Area of a Cylinder: Formula & Example

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  • 0:00 What is a Cylinder?
  • 0:20 The Surface Area of a Cylinder
  • 0:57 Calculating the Surface Area
  • 2:39 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll review the definition of a cylinder and learn how to find its surface area. Then, you can test your new knowledge with a brief quiz.

What is a Cylinder?

A cylinder is a three-dimensional object that consists of two circles joined together to form a round column:

drawing of a cylinder

So all the cans we have in our houses are cylinders. Columns are another real world example of cylinders.

The Surface Area of a Cylinder

How do we find a cylinder's surface area?

When we determine a cylinder's surface area, we're really adding together the area of the top and bottom circles and the area of the rectangle that forms the cylinder's side.

cylinder unfolded

The sum of the areas of the two circles and the rectangle is:

Formula showing the parts of the cylinder area

By combining like-terms, we can simplify this equation to:

area equals 2 pi r times r plus h

Calculating the Surface Area

Let's put this formula into action by finding the surface area of this cylinder:

cylinder with radius 4 inches and height 8 inches

We know from the diagram that the cylinder's radius is 4 inches, and the height is 8 inches. We can plug those values into our surface area formula. I will approximate pi to 3.14 throughout the lesson.

area equals 2 pi r times r plus h

A = (2 * 3.14 * 4) (4 + 8)

A = (25.12) (12)

A = 301.44

The cylinder's surface area is 301.44 square inches.

Example 2

But what about this cylinder?

cylinder with diameter 10 feet and height 100 feet

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