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Geometry: High School15 chapters | 160 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 why soda cans are cylinders and the method by which you can discover how much soda can fit inside by finding the volume. You will also learn about finding a cylinder's surface area.

Cylinders are popular shapes. Defined, a **cylinder** is a three-dimensional object with two round flat bases and one curved side. Picture a soda can and you are looking at a cylinder. These types of cans hold not only soda but also juices and other types of drinks as well. Walk into any grocery store and you will find tons of cylinders holding all kinds of goodies inside.

When it comes to cylinders, there are two measurements that you need to be concerned about. If you look at your soda cans, you will notice that they are all the same height and that the circles that make up the tops and bottoms are all the same size as well. This is because they have the same height as well as the same radius, which is the distance between the middle of the circle to the edge. It is these two measurements that determine the size of a cylinder. We label the height with *h* and the radius with *r* to make it easier for us when we are using the formulas for surface area and volume. Both formulas use both measurements.

The formula for surface area gives you the total area of all the surfaces together. Let's say you want to decorate your soda can with colorful wrapping paper. The formula for surface area will let you know how much paper you need. The formula looks like this:

Surface Area = 2 * pi * *r* * (*r* + *h*)

As long as you have your radius and height, you can go ahead and plug those values into your formula to find your answer for surface area. Let's see how this works if we have a soda can that is 6 inches high with a radius of 2 inches. We can label our *h* as 6 inches and our *r* as 2 inches. We then plug these numbers into our formula.

Surface Area = 2 * 3.14 * 2 * (2 + 6)

I've replaced the pi with its approximation of 3.14, and now all I need to do is to evaluate to find my answer. So I add the 2 and the 6 to get 8. I then multiply the 2 with the 3.14 with the 2 and then with the 8 to get my answer of 100.48 inches squared.

Surface Area = 2 * 3.14 * 2 * 8

Surface Area = 100.48 inches squared

My answer ends with my measuring unit squared, because area is always squared.

Now, if I wanted to find out how much soda the same soda can holds, I would use the formula for volume, the amount of space inside a three-dimensional object. The formula for the volume of a cylinder looks like this.

Volume = pi * *r*^2 * *h*

Again, if I had my radius and height, I can go ahead and plug those numbers in to find my answer. I already know that the soda can we are using has a height of 6 inches and a radius of 2 inches, so I can plug those numbers into the formula.

Volume = 3.14 * 2^2 * 6

I then go ahead and evaluate to find my answer. I square the 2 to get 4. I then multiply the 3.14, the 4, and the 6 together to get an answer of 75.36 inches cubed.

Volume = 3.14 * 4 * 6

Volume = 75.36 inches cubed

My answer here ends with my measuring units cubed, because volume is always cubed.

What have we learned? We've learned that **cylinders** are three-dimensional objects with two round flat bases and one curved side. Soda cans are real-world examples of cylinders. The only two measurements you need to find surface area and volume are the height and the radius. The formula for surface area is Surface Area = 2 * pi * *r* * (*r* + *h*), and the formula for volume is Volume = pi * *r*^2 * *h*. Once you have your height and radius, all you need is to plug in these numbers into your formula to find your answer.

After concluding this lesson, you should be able to:

- Define the 3-dimensional object- cylinder
- Understand the formulas for measuring cylinders
- Identify how to measure the volume of a cylinder

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Geometry: High School15 chapters | 160 lessons

- Planes and the Polyhedron: Definition and Example 3:52
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- Spheres: Definition, Area & Volume 5:22
- Go to High School Geometry: Geometric Solids

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