# Cylinder

You pop open a soft drink like the one below. Within a matter of minutes, you gulp down every last drop. Do you know how much you drank? As you can see, there isn’t any information on the can. However, you can find out using the volume formula for the cylinder. Most soft drink cans are in the shape of cylinders.

## What Is a Cylinder?

Now, you have seen what a cylinder is, but let’s see the requirements of a cylinder. First, a cylinder is 3-D. It isn’t a flat object. This shape contains circular bases that are parallel. A curved face is attached to these bases. In this case, a cylinder contains three faces. There are two round bases on either end of the curved face which encircles back to the beginning of the face.

Let’s look at some examples of objects that are known to have a cylinder shape.

Candles have a cylinder shape because they are flat on the top and bottom. These bases are circular, and they have a curved face.

The Greek Parthenon contains columns or pillars. The pillars or columns themselves are cylindrical in shape.

Finally, a jar is cylinder in shape. With the lid on, it has two flat and circular bases with a curved face in between.

See if you can identify any other objects that have a cylinder shape to them.

There are a few different types of cylinders. Let’s look at those few. There are the elliptic cylinder and oblique cylinder. So, what is the difference between them?

### Oblique Cylinder

In most cases like the jar and the soft drink can, the bases are parallel to each other, and the curved face is completely perpendicular to the bases. However, in an oblique cylinder, the cylinder leans to the side. The Leaning Tower of Pisa is a prime example of an oblique cylinder. This means that the curved base is not completely perpendicular to the bases since it leans.

### Elliptic Cylinder

An elliptic cylinder appears like a typical cylinder that has been stretched in the middle. The bases are not completely circular or round in shape. They have an elliptical shape like an egg. Some small office or bathroom trash cans would be considered elliptical cylinders. The opening of the trash cans are shaped like an egg.

## Find the Volume of a Cylinder

Since a cylinder is a 3-D shape, it can hold something like a liquid. Therefore, you can measure the volume of a cylinder. If you look at some examples of objects that are cylindrical in shape, you will notice that some of them hold liquid or a substance. For example, a soft drink can hold the soft drink. A jar may hold soup. Therefore, something can be poured into a container that is cylindrical in shape.

To find the volume of a cylinder, you need to use the formula below.

$$\mathrm\pi$$ is pi, and it is equal to 3.14. The “r” represents the radius of the cylinder, and the “h” represents the height of the cylinder.

The picture below of a cylinder shows the radius and height for this shape.

The radius is a line from the center of a circle to its edge. The measurement of the line usually shows this radius. The height is how tall the cylinder is. To calculate the volume of the cylinder, you will need to first identify the amounts for each part of the formula. First, pi, which represents the first symbol, is 3.14. The radius amount must be multiplied to itself. Then you begin to multiply 3.14 with the radius squared amount that you calculated. Then multiply that amount to the height. This will be your answer.

Example

Let’s do an example. Look at the example and see how the volume is calculated.

In this problem, you will multiply 3.14 for pi with the radius squared. The radius squared would be $$6^2$$ which means 6 is multiplied to itself, 6. So, 6 times 6 is 36. Now, multiply 3.14 times 36. The answer is 113.04. Then multiply your answer with the height, which is 10. The answer is 1,130.4. Therefore, the volume of this cylinder is $$1,130.4\;cm^2$$.

Most word problems about the volume of cylinders usually will ask you to determine how much liquid will fit into that cylindrical container. It could also want you to calculate other substances that would typically fit into that cylinder.

## The Surface Area of a Cylinder

The surface area of any shape is the area of the surface of each face of the shape. For a cylinder, we learned that it has 3 faces. Therefore, we need to calculate the area of each face, and then add them together. However, the best way to find the surface area of a cylinder would be to simply use the formula below.

Example

To better understand this, look at the example below.

First, we need to plug in the numbers from the example.

Then we need to multiply 2 times 3.14 times 4. This answer is 25.12. Then we will add the numbers, which are the height and radius, together. Six plus 4 equals 10. Last, we will multiply the two answers together. So, 25.12 times 10 equals 251.2. The surface area of this cylinder is 251.2 cm.