107 LearnersLast updated on July 9th, 2025
Volume of Cylinder Prism
The volume of a cylinder prism is the total space it occupies or the number of cubic units it can hold. A cylinder prism is a 3D shape with two parallel circular bases connected by a curved surface. To find the volume of a cylinder prism, we multiply the area of the base by its height. In real life, kids relate to the volume of a cylinder prism by thinking of things like a can, a drum, or a pipe. In this topic, let’s learn about the volume of a cylinder prism.
What is the volume of the cylinder prism?
The volume is the amount of space it occupies. It is calculated using the formula:
Volume = π × radius² × height
Where 'radius' is the radius of the circular base, and 'height' is the distance between the two bases.
A cylinder prism is a 3-dimensional shape with circular bases. To calculate its volume, multiply the area of the base (π × radius²) by the height of the cylinder.
Formula:
Volume = π × radius² × height
How to Derive the Volume of a Cylinder Prism?
To derive the volume of a cylinder prism, 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
prism: Base Area = π × radius²
The volume of a cylinder prism will be, Volume = π × radius² × height
How to find the volume of a cylinder prism?
The volume of a cylinder prism is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). Multiply the area of the base by the height to find the volume.
Let’s take a look at the formula for finding the volume of a cylinder prism:
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 circular bases.
Once we know the radius and height, substitute those values into the formula Volume = π × radius² × height
Tips and Tricks for Calculating the Volume of Cylinder Prism
Remember the formula: The formula for the volume of a cylinder prism 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 to find the volume.
Simplify the numbers: If the radius and height are simple numbers, it’s easy to calculate. For example, if radius = 3 and height = 5, then the volume is π × 3² × 5 = 45π.
Check for radius and height: Ensure you have the correct measurements for the radius and height before plugging them into the formula.
Common Mistakes and How to Avoid Them in Volume of Cylinder Prism
Making mistakes while learning the volume of a cylinder prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of cylinder prisms.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area is calculated by 2πrh + 2πr², whereas volume is calculated by multiplying the base area by the height. For example, the volume is π × radius² × height, not 2πrh + 2πr².
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the cylinder’s perimeter (circumference) instead of the volume formula. Volume is the space inside the cylinder prism, whereas the circumference is the distance around the base. 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 circular 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 miscalculate the given volume with solving for the radius or height. For example, if the volume is given, and they need to find the radius or height, they might forget to rearrange the formula correctly.
Volume of Cylinder Prism Examples
Problem 1
A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume?
The volume of the cylinder prism is 90π cm³.
Explanation
To find the volume of a cylinder prism, use the formula: V = π × radius² × height
Here, the radius is 3 cm and the height is 10 cm, so: V = π × 3² × 10 = 90π cm³
Problem 2
A cylinder has a radius of 5 m and a height of 7 m. Find its volume.
The volume of the cylinder prism is 175π m³.
Explanation
To find the volume of a cylinder prism, use the formula: V = π × radius² × height
Substitute the radius (5 m) and height (7 m): V = π × 5² × 7 = 175π m³
Problem 3
The volume of a cylinder is 200π cm³. What is the radius if the height is 8 cm?
The radius of the cylinder is 5 cm.
Explanation
If you know the volume of the cylinder and need to find the radius, rearrange the volume formula:
Volume = π × radius² × height
200π = π × radius² × 8
radius² = 25
radius = 5 cm
Problem 4
A cylinder has a radius of 2.5 inches and a height of 4 inches. Find its volume.
The volume of the cylinder prism is 25π inches³.
Explanation
Using the formula for volume:
V = π × radius² × height
Substitute the radius 2.5 inches and height 4 inches:
V = π × 2.5² × 4 = 25π inches³
Problem 5
You have a cylinder-shaped container with a radius of 3 feet and a height of 6 feet. How much space (in cubic feet) is available inside the container?
The container has a volume of 54π cubic feet.
Explanation
Using the formula for volume: V = π × radius² × height
Substitute the radius 3 feet and height 6 feet: V = π × 3² × 6 = 54π ft³
FAQs on Volume of Cylinder Prism
1.Is the volume of a cylinder prism 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?
4.Can the radius or height be a decimal or fraction?
5.Is the volume of a cylinder prism the same as the surface area?
Important Glossaries for Volume of Cylinder Prism
- Radius: The distance from the center of the cylinder's base to its edge.
- Height: The distance between the two parallel circular bases of the cylinder.
- Volume: The amount of space enclosed within a 3D object, calculated by multiplying the base area by the height. Expressed in cubic units (e.g., cm³, m³).
- Base Area: The area of the circular base, calculated as π × radius².
- Cubic Units: Units used to measure volume. If the radius is in cm, volume is in cm³; if in meters, volume is in 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
