So, in our tireless study of geometry, it’s time to consider the volume of a cylinder. The volume of a cylinder measures how much material can be stored inside it. More simply, it is the volume of space that the cylinder occupies. Do not forget that the cylinder has round bases and a height. The height determines its volume.
Here we learn about the formula to calculate the volume of a cylinder. We will also learn how to calculate the volume of hollow cylinders. This can be very useful. Get ready to learn all the details about cylinder volume with us. Use our knowledge to solve interesting problems!
How to Find the Volume of a Cylinder: Everything You Need to Know
So, let’s consider how you can find the volume of a cylinder and what formula is used for this. As you may remember, the volume of a prism is calculated by taking into account the area of its base multiplied by its height. And the cylinder, in fact, can be imagined as a prism with round bases. So why not apply the same formula?
So, the formula for the volume of a right cylinder is reduced to the product of the circle’s area and its height. Thus, it looks like this:
Note: the formula for the volume of an slanted cylinder is the same as for the right one. This formula is also based on the area of the base and the height of the cylinder. Therefore, the formula V=π⋅R2⋅h remains unchanged.
Volume of an elliptical cylinder
Now let’s talk about the volume of an elliptical cylinder. It depends on the area of the ellipse and its height. So, the formula for the volume of an elliptical cylinder looks like this:
Volume of a hollow cylinder
And if the cylinder is empty inside? For such a situation, we have a separate formula that takes into account the difference between the volume of the outer and inner cylinder. So, the formula for the volume of a hollow cylinder looks like this:
Note that this formula is equivalent to calculating the volume of an entire cylinder with subsequent subtraction of the volume of the inner cylinder.
Volume of a Cylinder in Practice: Examples with 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 volume of a cylinder with a radius of 5 cm and a height of 10 cm?
So, according to the condition of the problem, we have the following values: radius R=5 and height h=10. Using the volume formula with the following values, we get:
Thus, the volume of the cylinder is 785 cm3.
Example 2: What is the volume of a cylinder with a diameter of 12 cm and a height of 11 cm?
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=12/2=6 and height h=11. Substituting these values into our formula, we will have:
Thus, the volume of the cylinder is 1243.44 cm3.
Example 3: What is the volume of a hollow cylinder whose height is 20 cm, inner radius 6 cm and outer radius 8 cm?
According to the condition of the problem, we have the following values: radius of the outer cylinder R1=8, radius of the inner cylinder R2=6 and height h=20. Using these values in the formula for the volume of a hollow cylinder, we have:
Therefore, the volume of the cylinder is 1758.4 см3.
Deeper into Cylinder Geometry: Additional Topics for Study
We invite you to learn more about the cylinder and its properties! In addition to the volume formulas that we have considered, the following topics are interesting to study:
- What is a cylinder: Properties, formulas and examples – Learn more about the main properties of a cylinder, learn different formulas and consider interesting examples.
- Diameter of a cylinder: Formulas and examples – Discover the role of diameter in measuring a cylinder, learn the relevant formulas and apply them to various examples.
- Total surface area of a cylinder: Formula and examples – Explore in depth how the total surface area of a cylinder is calculated, study the relevant formulas and analyze examples for better understanding.
Geometric Calculations in Programming: Flowchart for Calculating the Volume of a Cylinder
