The diameter of a cylinder is the largest line passing through the center of the circles forming its bases. It is a key parameter for calculations in geometry. Knowing the diameter, we can determine the volume, surface area and other characteristics of the cylinder.
In this article, we will consider three methods of determining the diameter of a cylinder and analyze practical examples of its application. Ready to learn more about this interesting and useful geometric parameter? Then let’s continue!
Diameter of a Cylinder: Calculation Methods and Formulas
So, as we have already found out, radius and height are the main dimensions of a cylinder that we often use. But what if we need to find the diameter? Well, everything is simple, my friend! If we know the radius, we just need to double it, and we get the diameter.
So the formula for this looks like this:
Finding the diameter of a cylinder using the volume
Now let’s see how we can determine the diameter if we have the volume. Do you remember the formula for the volume of a cylinder? It looks like V=π⋅R2⋅h. So, if we want to determine the diameter, we can transform this formula and get something like:
Thus, if we know the volume and the height, we can use this formula to find the diameter.
Finding the diameter of a cylinder by surface area
There is another way to find the diameter if we know the surface area of the cylinder. Here the formula is a little more complicated, but don’t worry, we’ll figure it out together with you! The formula for surface area looks like this: TSA=2⋅π⋅R⋅(h+R). But in terms of diameter, it will look like this:
Thus, if we know the surface area and the height, we can use this formula to find the diameter of the cylinder.
Diameter of a Cylinder in Action: Examples and Answers
The above formulas are used to solve the following examples. Each example has a corresponding solution, but it is recommended that you try to solve them yourself before looking at the answer.
Example 1: What is the diameter of a cylinder whose radius is 5 cm?
So, by the condition of the problem, we have that the radius R=5. Using the above formula with the following value, we get:
Thus, the diameter of a cylinder is 10 cm.
Example 2: What is the diameter of a cylinder with a volume of 100 cubic cm and a height of 8 cm?
In this case, we have the following values: volume V=100 and height h=8. Therefore, we use the volume formula, substitute the given values and find D:
Thus, the diameter of a cylinder is 4 cm.
Example 3: What is the diameter of a cylinder with a surface area of 100 square cm and a height of 4 cm?
According to the condition of the problem, we have the following values: TSA=100 and height h=4. Using them in the formula of the total surface area in terms of diameter, we have:
Note that as a result we got a quadratic equation. Let’s apply the quadratic formula to find the solution:
A quadratic equation usually has two solutions. However, in this case, a negative value does not make sense for the diameter, so we consider only the positive solution. So, the diameter of a cylinder is 4.93 cm.
Deeper into Cylinder Geometry: Additional Topics for Study
This section will be of interest to those who want to study the topic of the cylinder even more deeply. Suggested topics for further research include:
- What is a cylinder: Properties, formulas and examples – Wondering what a cylinder is? Let’s understand its main properties, get acquainted with various formulas and look at examples.
- Total surface area of a cylinder: Formula and examples – How is the total surface area of a cylinder calculated? Let’s dive deeper into this topic, learn the relevant formulas and analyze the examples for a better understanding.
- Volume of a cylinder: Formulas and examples – What is involved in calculating the volume of a cylinder? How can this be applied in practice? Let’s look at formulas and problem solutions to better understand this process.
Quickly Determine Cylinder Diameter: An Easy-to-Follow Flowchart
