Surface area of a cylinder

To derive the formula of the surface area of a cylinder, we will start by showing you how you can make a cylinder :




Start with a rectangle and two circles

Template of a cylinder


Then, fold the rectangle until you make an open cylinder with it. An open cylinder is a cylinder that has no bases. A good real life example of an open cylinder is a pipe used to flow water if you have seen one before



Folded rectangle


Next, using the two circles as bases for the cylinder, put one on top of the cylinder and put one beneath it.

Two circle and a folded rectangle will make a cylinder


Of course, the two circles will have the exact same size or the same diameter as the circles obtained by folding the rectangle

You Finally, you end up with your cylinder!

Cylinder made with 2 circlea and a folded rectangle


Now, what did we go through so much trouble? Well if you can make the cylinder with the rectangle and the two circles, you can use them to derive the surface area of the cylinder. Does that make sense?



The area of the two circles is straightforward. The area of one circle is pi × r2, so for two circles, you get 2 × pi × r2

To find the area of the rectangle is a little bit tricky and subtle!

Let us take a closer look at our rectangle again.



Cylinder template
Thus, the longest side or folded side of the rectangle must be equal to 2 × pi × r, which is the circumference of the circle

To get the area of the rectangle, multiply h by 2 × pi × r and that is equal to 2 × pi × r × h

Therefore, the total surface area of the cylinder, call it SA is:

SA = 2 × pi × r2  +   2 × pi × r × h

Example #1:


Find the surface area of a cylinder with a radius of 2 cm, and a height of 1 cm

SA = 2 × pi × r2  +   2 × pi × r × h

SA = 2 × 3.14 × 22  +   2 × 3.14 × 2 × 1

SA = 6.28 × 4  +   6.28 × 2

SA = 25.12 + 12.56

Surface area = 37.68 cm2


Example #2:


Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm

SA = 2 × pi × r2  +   2 × pi × r × h

SA = 2 × 3.14 × 42  +   2 × 3.14 × 4 × 3

SA = 6.28 × 16  +   6.28 × 12

SA = 100.48 + 75.36

Surface area = 175.84 cm2






Recent Articles

  1. Factoring Quadratic Equations Worksheet

    Oct 17, 17 05:34 PM

    Factoring quadratic equations worksheet-get some practice factoring quadratic equations

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Page copy protected against web site content infringement by Copyscape





Recent Lessons

  1. Factoring Quadratic Equations Worksheet

    Oct 17, 17 05:34 PM

    Factoring quadratic equations worksheet-get some practice factoring quadratic equations

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz