How to Find Surface Area of a Cylinder

How to Find Surface Area of a Cylinder
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  • 0:02 A Cylinder
  • 0:41 The Surface Area
  • 1:11 The Formula
  • 2:16 Using the Formula
  • 3:49 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn the formula you can use to find the surface area of a cylinder. Learn the measurements that you'll need as well as how to use them.

A Cylinder

In this video lesson, we talk about cylinders. What are they? We can define a cylinder as a straight, round bar. In math terms, a cylinder is defined as two parallel, flat, circular surfaces at either end of a curved section. I don't know about you, but it's easier for me to think of a cylinder as a straight, round bar. That's what they look like.

Picture a soda can, and you have a cylinder. Basic candles are also cylinders. What do they all look like? They all just look like straight, round bars. You can grab the 'bar' in the middle curved section, and these 'bars' have circular ends that are flat and parallel to each other.

The Surface Area

The surface area comes in when we consider the outside area. You can think of the surface area as the amount of wrapping paper you would need to completely cover a cylinder. Say you want to surprise your best friend with her favorite soda. You would want to wrap it up nicely with some nice wrapping paper. You might perhaps add a nice bow to it, too. If you need to buy some wrapping paper at the store, you first need to calculate the surface area of your cylinder to make sure that you are buying enough wrapping paper to cover your soda can.

The Formula

To help you do that, we of course have a formula! Isn't math great? We have a formula for almost everything and anything! Our formula to find the surface area of our cylinder is 2 times pi times the radius times the height plus 2 times pi times the radius squared.

cylinder surface area

This formula is actually the combination of two calculations. We first calculate the surface area of the curved part and then we add the two surface areas of our circles. If you ever forget this surface area formula for cylinders, you can always break apart your cylinder into its curved area and flat areas to find the surface area of each area separately before adding them.

Looking at our formula, we see that we need the radius and height measurement of our cylinder. That's not bad. We only need to know two measurements. In the real world, we can always measure our object. Usually, when working with math problems, you are given the measurements that you need. So for our problem, we are given that our height is 4.8 inches and our radius is 1.25 inches.

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