Why do we need to know what is a surface area of a cylinder? Let’s say you want to understand how to determine how much area this geometric object occupies in three-dimensional space. Don’t worry if such questions arise – we are here to help you.
So what is a cylinder? According to our geometric knowledge, a cylinder consists of two circular bases and a surface covering these bases. To calculate the area of this surface, we need to take the area of both circular bases and add to it the area of the lateral surface. Here we’re going to look at the formula for this and solve a few examples to demonstrate how it works in practice. So, get ready to increase your cylinder knowledge!
Formula for Surface Area of a Cylinder: Everything You Need to Know
So, as we have already mentioned, the total surface area of a cylinder consists of two main components: the area of its bases and the area of its lateral surface.
Base surface area of a cylinder
Imagine that the cylinder is just a pair of circles that you see from above and below. Therefore, to find the area of both these circles, we can use the formula for the area of a circle. After all, they both have the shape of a circle. So, the formula for the area of the base of the cylinder is as follows:
Curved surface area of a cylinder
Now let’s look at the curved side of the cylinder that connects the two circular bases. This surface reminds you of a rectangle wrapped around a cylinder.
To find its area, we use the formula of the length of a rectangle multiplied by its width. But in this case, our “length” is the length of the circle, and “width” is the height of the cylinder. So, the formula for the area of the curved surface of a cylinder looks like this:
Total surface area of the cylinder
Now that we know the areas of both component parts of the cylinder, we can calculate its total surface area. Simply add the area of both bases and the area of the curved surface together. So, the formula for the total surface area of a cylinder will be:
Surface Area of a Cylinder: Examples and Solutions
It’s time to consider a few examples that will help us better understand how to calculate the total surface area of a cylinder using the formula in question. Ready to take the challenge?
Example 1: What is the surface area of a cylinder with a radius of 5 cm and a height of 8 cm?
So, according to the condition of the problem, we have the following values: radius R=5 and height h=8. Using the surface area formula with the following values, we get:
Thus, the total surface area of the cylinder is 408.2 cm2.
Example 2: If a cylinder has a diameter of 6 cm and a height of 7 cm, what is its surface area?
In this case, we have a diameter instead of a radius. However, we can get the radius by simply dividing the diameter by 2. So we have: radius R=6/2=3 and height h=7. Substituting these values into our formula, we will have:
Therefore, the surface area of the cylinder is 188.4 cm2.
Example 3: What is the surface area of a cylinder with a diameter of 12 cm and a height of 15 cm?
Similar to the previous example, divide the diameter by 2 to get the radius. So, we have: radius R=12/2=6 and height h=15. Using these values in the formula for the surface area, we have:
Thus, the total surface area of the cylinder is 791.28 cm2.
Learn More: Additional Cylinder Geometry Topics Awaiting You!
That’s not all there is to know about the cylinder! If you are interested in this geometric shape, then you will definitely be interested in learning more about the following topics:
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- What is a cylinder: Properties, formulas and examples – Let’s take a closer look at the properties of a cylinder and the main formulas that will help you better understand this geometric figure. Examples will help consolidate knowledge.
- Diameter of a cylinder: Formulas and examples – Cylinder diameter is another important parameter to consider. We learn how to calculate the diameter, which formulas are used and how it is applied on examples.
- Volume of a cylinder: Formulas and examples – Cylinder volume is another important characteristic that should be considered in more detail. Let’s learn formulas for calculating the volume of a cylinder and solve several interesting problems to consolidate knowledge.
Programming of Geometric Calculations: Flowchart of the Algorithm for Calculation of the Surface Area of a Cylinder
