110 LearnersLast updated on July 11th, 2025
Volume of Circular Prism
The volume of a circular prism, commonly referred to as a cylinder, is the total space it occupies or the number of cubic units it can hold. A circular prism is a 3D shape with two parallel circular bases connected by a curved surface. To find the volume of a circular prism, we multiply the area of its base by its height. In real life, kids relate to the volume of a circular prism by thinking of things like a can of soup or a tube of toothpaste. In this topic, let’s learn about the volume of the circular prism.
What is the volume of a circular prism?
The volume of a circular prism is the amount of space it occupies. It is calculated by using the formula: Volume = π × radius² × height Where ‘radius’ is the radius of the circular base and ‘height’ is the distance between the bases.
Volume of Circular Prism Formula A circular prism is a 3-dimensional shape with circular bases. To calculate its volume, you multiply the area of the base (π × radius²) by the height.
The formula for the volume of a circular prism is given as follows: Volume = π × radius² × height
How to Derive the Volume of a Circular Prism?
To derive the volume of a circular prism, we use the concept of volume as the total space occupied by a 3D object.
Since a circular prism has circular bases, its volume can be derived as follows:
The formula for the volume is: Volume = Base Area × Height
For a circular base: Base Area = π × radius²
The volume of a circular prism will be, Volume = π × radius² × height
How to find the volume of a circular prism?
The volume of a circular 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 circular prism:
Write down the formula Volume = π × radius² × height
The radius is the distance from the center to the edge of the base. The height is the distance between the bases. Once we know the radius and height,
substitute those values in the formula Volume = π × radius² × height To find the volume, calculate the base area and multiply by the height.
Tips and Tricks for Calculating the Volume of Circular Prism
Remember the formula: The formula for the volume of a circular prism is: Volume = π × radius² × height
Break it down: The volume is how much space fits inside the circular prism. Calculate the area of the base and multiply by the height.
Simplify the numbers: If the radius is a simple number like 2, 3, or 4, it is easy to square, then multiply by the height. Check for height and radius Ensure you have the correct measurements for both the height and the radius to avoid errors.
Common Mistakes and How to Avoid Them in Volume of Circular Prism
Making mistakes while learning the volume of the circular prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of circular 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 differently, whereas volume is calculated by multiplying the base area by the height. For example, the volume is π × radius² × height, not the surface area formula.
Mistake 2
Confusing Volume with Circumference
Some kids may think of the circumference of the base instead of the volume formula. Volume is the space inside the circular prism, whereas circumference refers to 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 circular prism 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 miscalculate the given measurements when solving for volume. For example, if the radius or height is given, ensure those values are accurate before calculating the volume.
Volume of Circular Prism 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 141.37 cm³ (rounded to two decimal places).
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 ≈ 141.37 cm³
Problem 2
A circular prism has a radius of 7 m and a height of 10 m. Find its volume.
The volume of the circular prism is 1539.38 m³ (rounded to two decimal places).
Explanation
To find the volume of a circular prism, use the formula: V = π × radius² × height
Substitute the radius (7 m) and height (10 m):
V = π × 7² × 10 ≈ 1539.38 m³
Problem 3
The volume of a circular prism is 314 cm³. If the radius is 5 cm, what is the height of the prism?
The height of the circular prism is 4 cm.
Explanation
If you know the volume and radius of the circular prism, you can find the height using the formula:
V = π × radius² × height 314 = π × 5² × height
Height = 314 / (π × 25) ≈ 4 cm
Problem 4
A circular prism has a radius of 2.5 inches and a height of 8 inches. Find its volume.
The volume of the circular prism is 157.08 inches³ (rounded to two decimal places).
Explanation
Using the formula for volume: V = π × radius² × height
Substitute the radius (2.5 inches) and height (8 inches):
V = π × 2.5² × 8 ≈ 157.08 inches³
Problem 5
You have a cylindrical container with a radius of 4 feet and a height of 6 feet. How much space (in cubic feet) is available inside the container?
The container has a volume of 301.59 cubic feet (rounded to two decimal places).
Explanation
Using the formula for volume: V = π × radius² × height
Substitute the radius (4 feet) and height (6 feet): V = π × 4² × 6 ≈ 301.59 ft³
FAQs on Volume of Circular Prism
1.Is the volume of a circular 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 height?
4.Can the radius or height be a decimal or fraction?
Important Glossaries for Volume of Circular Prism
- Radius: The distance from the center to the edge of the circular base.
- Height: The distance between the two parallel bases of the circular prism.
- Volume: The amount of space enclosed within a 3D object. In the case of a circular prism, the volume is calculated by multiplying the base area by the height. It is expressed in cubic units (e.g., cm³, m³).
- Base Area: The area of the circular base, calculated as π × radius².
- Cubic Units: The units of measurement used for volume. If the radius and height 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
