103 LearnersLast updated on July 21st, 2025
Volume of Right Circular Cylinder
The volume of a right circular 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 connected by a curved surface. To find the volume of a cylinder, we multiply the area of its base by its height. In real life, one can relate to the volume of a cylinder by thinking of things like a can of soup, a drum, or a fire extinguisher. In this topic, let’s learn about the volume of the cylinder.
What is the volume of the cylinder?
The volume of a right circular cylinder is the amount of space it occupies.
It is calculated by using the formula: Volume = πr²h Where ‘r’ is the radius of the base, and ‘h’ is the height of the cylinder.
Volume of Cylinder Formula A cylinder is a 3-dimensional shape with two parallel circular bases.
To calculate its volume, you multiply the area of the base (πr²) by the height (h).
The formula for the volume of a cylinder is given as follows: Volume = πr²h
How to Derive the Volume of a Cylinder?
To derive the volume of a right circular 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 a cylinder is: Volume = Area of Base x Height For a cylinder: Area of Base = πr² (where r is the radius of the base)
The volume of a cylinder will be, Volume = πr² x h
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). 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: Write down the formula Volume = πr²h The radius is the distance from the center to the edge of the base.
The height is the distance between the two bases. Once we know the radius and the height, substitute those values into the formula volume = πr²h To find the volume, calculate the area of the base and multiply it by the height.
Tips and Tricks for Calculating the Volume of Cylinder
Remember the formula: The formula for the volume of a cylinder is: Volume = πr²h Break it down: The volume is how much space fits inside the cylinder. You need to find the base area (πr²) and multiply it by the height.
Simplify the numbers: If the radius and height are simple numbers, it is easy to calculate.
For example, if r = 3 and h = 4, then the volume is π(3)²(4) = 36π.
Use π as 3.14 for quick calculations, but use the π button on a calculator for more precision.
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 includes the lateral area and the area of the bases, but volume is calculated by multiplying the base area by the height.
For example, the volume is πr²h, not 2πrh + 2πr².
Mistake 2
Confusing Volume with Circumference
Some learners may think of the cylinder’s circumference instead of the volume formula.
Volume is the space inside the cylinder, whereas circumference refers to the distance around the circular base.
Do not mix them up.
Mistake 3
Using the wrong Formula for rectangular prisms
Some learners use the formula for the volume of a rectangular prism (length x width x height) instead of the cylinder formula πr²h.
Mistake 4
Confusing linear measurements with cubic volume
Thinking of volume in terms of linear measurements.
This happens when someone uses just the height or radius instead of understanding that volume relates to cubic measurements involving both radius and height.
Mistake 5
Incorrectly calculating the radius
Some students calculate the given volume with solving for the radius. For example, if the volume is given, and they need to find the radius, they might forget to rearrange the formula properly to solve for r.
Volume of 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 141.3 cm³.
Explanation
To find the volume of a cylinder, use the formula: V = πr²h Here, the radius is 3 cm and the height is 5 cm, so: V = π(3)²(5) = 45π ≈ 141.3 cm³
Problem 2
A cylinder has a radius of 7 m and a height of 10 m. Find its volume.
The volume of the cylinder is 1540 m³.
Explanation
To find the volume of a cylinder, use the formula: V = πr²h Substitute the radius (7 m) and height (10 m): V = π(7)²(10) = 490π ≈ 1540 m³
Problem 3
The volume of a cylinder is 314 cm³ and its height is 4 cm. What is the radius of the cylinder?
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 formula: V = πr²h 314 = πr²(4) r² = 314 / (4π) ≈ 25 r = √25 = 5 cm
Problem 4
A cylinder has a radius of 2.5 inches and a height of 6 inches. Find its volume.
The volume of the cylinder is 117.8 inches³.
Explanation
Using the formula for volume: V = πr²h Substitute the radius 2.5 inches and height 6 inches: V = π(2.5)²(6) = 37.5π ≈ 117.8 inches³
Problem 5
You have a cylindrical tank with a radius of 4 feet and a height of 8 feet. How much water (in cubic feet) can the tank hold?
The tank can hold 402.1 cubic feet of water.
Explanation
Using the formula for volume: V = πr²h Substitute the radius 4 feet and height 8 feet: V = π(4)²(8) = 128π ≈ 402.1 ft³
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 radius?
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 to the edge of the base of the cylinder.
- Height: The perpendicular distance between the two circular bases of the cylinder.
- Volume: The amount of space enclosed within a 3D object, calculated for a cylinder by multiplying the base area by the height.
- Base Area: The area of the circular base of the cylinder, given by πr².
- Cubic Units: The units of measurement used for volume, such as cubic centimeters (cm³) or 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
