108 LearnersLast updated on July 11th, 2025
Volume of Cylinder in Cubic Feet
The volume of a cylinder is the total space it occupies or the number 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 multiply the area of its base by its height. In real life, kids relate to the volume of a cylinder by thinking of things like a can of soda, a drum, or a pipe. In this topic, let’s learn about the volume of a cylinder in cubic feet.
What is the volume of a cylinder?
The volume of a cylinder 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 Cylinder Formula A cylinder is a 3-dimensional shape with two parallel circular bases.
To calculate its volume, multiply the area of the base (π × radius²) by the height.
The formula for the volume of a cylinder is given as follows: Volume = π × radius² × height
How to Derive the Volume of a Cylinder?
To derive the volume of a cylinder, we use the concept of volume as the total space occupied by a 3D object.
The volume can be derived as follows:
The formula for the volume of a cylinder is: Volume = Base Area × Height
For a cylinder: Base Area = π × radius²
Height = h The volume of a cylinder will be, Volume = π × radius² × height
How to find the volume of a cylinder?
The volume of a cylinder is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). Calculate the base area and multiply it by the height 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 to the edge of the base. The height of a cylinder 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, calculate π × radius², then multiply by the height.
Tips and Tricks for Calculating the Volume of 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. You need to calculate the base area first and then multiply by the height.
Simplify the numbers: If the radius and height are simple numbers, calculating the volume becomes straightforward.
Use approximations for π: If exact values aren’t needed, approximate π as 3.14 to simplify calculations.
Common Mistakes and How to Avoid Them in Volume of 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 is calculated by 2πrh + 2πr², but volume is calculated by π × radius² × height.
Mistake 2
Mistaking Diameter for Radius
Some kids may confuse radius with diameter. Remember that the radius is half the diameter. Use the correct value in the formula.
Mistake 3
Using the wrong Formula for other shapes
Some kids use the formula for volume of a rectangular prism (length × width × height) instead of the cylinder formula.
Mistake 4
Incorrectly calculating the base area
Some students incorrectly calculate the base area. Remember that the base area of a cylinder is a circle, calculated as π × radius².
Mistake 5
Forgetting to multiply by height
Some students calculate the base area but forget to multiply it by the height to find the volume.
Volume of Cylinder Examples
Problem 1
A cylinder has a radius of 2 feet and a height of 5 feet. What is its volume?
The volume of the cylinder is approximately 62.8 cubic feet.
Explanation
To find the volume of a cylinder, use the formula: V = π × radius² × height
Here, the radius is 2 feet and the height is 5 feet,
so: V = π × 2² × 5 ≈ 3.14 × 4 × 5 = 62.8 cubic feet
Problem 2
A cylinder has a radius of 3 feet and a height of 10 feet. Find its volume.
The volume of the cylinder is approximately 282.6 cubic feet.
Explanation
To find the volume of a cylinder, use the formula: V = π × radius² × height
Substitute the radius (3 feet) and height (10 feet):
V = π × 3² × 10 ≈ 3.14 × 9 × 10 = 282.6 cubic feet
Problem 3
The volume of a cylinder is 150 cubic feet, and its radius is 3 feet. What is the height of the cylinder?
The height of the cylinder is approximately 5.3 feet.
Explanation
If you know the volume of the cylinder and need to find the height, use the formula: Volume = π × radius² × height
Rearrange to find height: Height = Volume / (π × radius²) Height ≈ 150 / (3.14 × 9) ≈ 5.3 feet
Problem 4
A cylinder has a radius of 4 inches and a height of 6 inches. Find its volume.
The volume of the cylinder is approximately 301.44 cubic inches.
Explanation
Using the formula for volume: V = π × radius² × height
Substitute the radius 4 inches and height 6 inches: V = π × 4² × 6 ≈ 3.14 × 16 × 6 = 301.44 cubic inches
Problem 5
You have a cylindrical water tank with a radius of 5 feet and a height of 12 feet. How much water (in cubic feet) can the tank hold?
The tank can hold approximately 942 cubic feet of water.
Explanation
Using the formula for volume: V = π × radius² × height
Substitute the radius 5 feet and height 12 feet: V = π × 5² × 12 ≈ 3.14 × 25 × 12 = 942 cubic feet
FAQs on Volume of 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 height?
4.Can the radius be a decimal or fraction?
5.Is the volume of a cylinder the same as the surface area?
Important Glossaries for Volume of Cylinder
- Radius: The distance from the center of the base to the edge of the circular base.
- Height: The distance between the two parallel bases of the cylinder.
- Volume: The amount of space enclosed within a 3D object like a cylinder. It is calculated by π × radius² × height and is expressed in cubic units (e.g., ft³).
- Base Area: The area of the circular base of the cylinder, calculated as π × radius².
- Cubic Units: The units of measurement used for volume. If the radius and height are in feet, the volume will be in cubic feet (ft³).
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
