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Basic Geometry: Help & Review16 chapters | 109 lessons

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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.

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** 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.

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.

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.

Once we have the measurements that we need, we can label each measurement with its appropriate letter. So, we label the height with *h* and the radius with *r*. We can then replace these letters in the formula with their values. We replace the *r* with 1.25 and the *h* with 4.8. Everything else in the formula stays the same. We now have our surface area equals 2 times pi, or 3.14, times 1.25 times 4.8 plus 2 times pi, or 3.14, times 1.25 squared.

Our next and final step is to evaluate. We multiply everything out and add them up.

After evaluating everything, we get an answer of 47.4925 square inches. We recall that the surface area always ends with our units squared. We also remember that if some of our measurements are different units from the other, then we need to convert the units so that they are all the same. So, if one measurement is in inches and the other measurement is in feet, then we need to convert either the inches to feet or the feet to inches. In our case, both measurements are in inches so we don't need to convert either of them.

So, we need 47.4925 square inches of wrapping paper to completely cover the soda can. At the store, then, we look for wrapping papers with more than 47.4925 square inches. Ah, this one will do. It has 200 square inches to it. That's plenty! We can cover four soda cans with this one.

Let's review what we've learned, now. We've learned that a **cylinder** is a straight, round bar. A soda can is a real world example of a cylinder. The **surface area** of our cylinder is the outside area. The formula for the surface area of a cylinder is 2 times pi times the radius times the height plus 2 times pi times the radius squared. To use this formula, we plug in our radius measurement and height measurement. We then evaluate to find our answer.

Now that you are done with this lesson you should be able to recall the equation for and calculate the surface area of a cylinder.

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Basic Geometry: Help & Review16 chapters | 109 lessons

- Points, Lines & Angles in Geometry 5:13
- Overview of the Basic Shapes in Geometry 3:46
- Vertical Angles & Complementary Angles: Definition & Examples 4:17
- Overview of Three-dimensional Shapes in Geometry 3:28
- How to Find Surface Area of a Cube and a Rectangular Prism 4:08
- How to Find Surface Area of a Cylinder 4:26
- Combined Figures: Perimeter, Area, and Volume 5:38
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