102 LearnersLast updated on September 5, 2025
Volume of Vertical Cylinder
The volume of a vertical cylinder is the total space it occupies or the amount of cubic units it can hold. A cylinder is a 3D shape with two parallel circular bases and a curved surface connecting them. To find the volume of a cylinder, we use the formula involving its radius and height. In real life, kids can relate to the volume of a cylinder by thinking of objects like a can of soup, a glass of water, or a drum. In this topic, let’s learn about the volume of a vertical cylinder.
What is the volume of a vertical cylinder?
The volume of a vertical cylinder is the amount of space it occupies. It is calculated using the formula:
Volume = π × radius² × height Where 'radius' is the radius of the base of the cylinder, and 'height' is the vertical distance between the bases.
Volume of Cylinder Formula : A cylinder is a 3-dimensional shape with circular bases. To calculate its volume, you multiply the area of the base (π × radius²) by the height of the cylinder.
The formula for the volume of a cylinder is given as follows: Volume = π × radius² × height
How to Derive the Volume of a Vertical Cylinder?
To derive the volume of a vertical cylinder, we use the concept of volume as the total space occupied by a 3D object.
Since a cylinder has a circular base, its volume can be derived as follows: The formula for the volume of any prism is: Volume = Base Area × Height
For a cylinder: Base Area = π × radius² (since the base is a circle)
The volume of a cylinder will be, Volume = π × radius² × height
How to find the volume of a vertical cylinder?
The volume of a cylinder is always expressed in cubic units, for example, cubic centimeters cm³, cubic meters m³. Use the radius and height, and apply them in the formula to find the volume.
Let’s take a look at the formula for finding the volume of a cylinder:
Write down the formula Volume = π × radius² × height
The radius is the distance from the center of the base to its edge. The height is the distance between the two bases.
Once we know the radius and height, substitute those values in the formula Volume = π × radius² × height To find the volume, multiply the area of the base by the height of the cylinder.
Tips and Tricks for Calculating the Volume of Vertical Cylinder
Remember the formula: The formula for the volume of a cylinder is simple: Volume = π × radius² × height
Break it down: The volume is how much space fits inside the cylinder. Multiply the area of the base by the height.
Simplify the numbers: If the radius or height is a simple number, it becomes easier to calculate. For example, if the radius is 3, then the base area is 3² = 9π. Check for square roots If you are given the volume and need to find the radius or height, you might need to work backwards. For example, if the volume is given and you need to find the radius, you may need to solve for the square root.
Common Mistakes and How to Avoid Them in Volume of Vertical Cylinder
Making mistakes while learning the volume of the cylinder is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of cylinders.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves calculating the area of both the bases and the curved surface area, but volume is calculated by multiplying the base area by the height. For example, the volume is π × radius² × height, not 2 × π × radius × (radius + height).
Mistake 2
Confusing Volume with Lateral Surface Area
Some kids may think of the lateral surface area instead of the volume formula. Volume is the space inside the cylinder, whereas lateral surface area refers to the area of the curved surface only. Do not mix them up.
Mistake 3
Using the wrong Formula for rectangular prisms
Some kids use the formula for the volume of a rectangular prism (length × width × height) instead of the cylinder formula.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements. This happens when someone uses the radius or height (which are linear measurements) instead of understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the radius or height
Some students calculate the given volume with solving for the radius or height. For example, if the volume is given, and they need to find the radius, they might forget to solve for the square root of the area.
Volume of Vertical Cylinder Examples
Problem 1
A cylinder has a radius of 3 cm and a height of 5 cm. What is its volume?
The volume of the cylinder is approximately 141.37 cm³.
Explanation
To find the volume of a cylinder, use the formula: V = π × radius² × height
Here, the radius is 3 cm and the height is 5 cm, so: V = π × 3² × 5 ≈ 3.1416 × 9 × 5 ≈ 141.37 cm³
Problem 2
A cylinder has a radius of 2 m and a height of 10 m. Find its volume.
The volume of the cylinder is approximately 125.66 m³.
Explanation
To find the volume of a cylinder, use the formula: V = π × radius² × height
Substitute the radius (2 m) and height (10 m): V = π × 2² × 10 ≈ 3.1416 × 4 × 10 ≈ 125.66 m³
Problem 3
The volume of a cylinder is 314.16 cm³. The radius is 2 cm. What is the height of the cylinder?
The height of the cylinder is approximately 25 cm.
Explanation
If you know the volume of the cylinder and the radius, you can find the height by rearranging the volume formula:
Volume = π × radius² × height 314.16 = π × 2² × height height = 314.16 / (π × 4) ≈ 25 cm
Problem 4
A cylinder has a radius of 4 inches and a height of 3 inches. Find its volume.
The volume of the cylinder is approximately 150.80 inches³.
Explanation
Using the formula for volume: V = π × radius² × height
Substitute the radius 4 inches and height 3 inches: V = π × 4² × 3 ≈ 3.1416 × 16 × 3 ≈ 150.80 inches³
Problem 5
You have a cylindrical container with a radius of 6 feet and a height of 2 feet. How much space (in cubic feet) is available inside the container?
The container has a volume of approximately 226.20 cubic feet.
Explanation
Using the formula for volume: V = π × radius² × height
Substitute the radius 6 feet and height 2 feet: V = π × 6² × 2 ≈ 3.1416 × 36 × 2 ≈ 226.20 ft³
FAQs on Volume of Vertical Cylinder
1.Is the volume of a cylinder the same as the surface area?
2.How do you find the volume if the radius and height are given?
3.What if I have the volume and need to find the radius or height?
4.Can the radius or height be a decimal or fraction?
5.Is the volume of a cylinder the same as the surface area?
Important Glossaries for Volume of Vertical Cylinder
- Radius: The distance from the center of the base of the cylinder to its edge. It is half of the diameter of the base.
- Height: The vertical distance between the two bases of the cylinder.
- Volume: The amount of space enclosed within a 3D object. In the case of a cylinder, the volume is calculated using the formula π × radius² × height. It is expressed in cubic units (e.g., cm³, m³).
- π (Pi): A mathematical constant approximately equal to 3.1416, representing the ratio of a circle's circumference to its diameter.
- Cubic Units: The units of measurement used for volume. If the dimensions are in centimeters (cm), the volume will be in cubic centimeters (cm³); if in meters, it will be in cubic meters (m³).
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
