105 LearnersLast updated on July 9th, 2025
Volume of Half Cylinder
The volume of a half cylinder is the total space it occupies or the number of cubic units it can hold. A half cylinder is a 3D shape consisting of a cylinder cut in half along its vertical axis. To find the volume of a half cylinder, we first find the volume of the full cylinder and then divide it by two. In real life, kids relate to the volume of a half cylinder by thinking of things like a half pipe or a semi-circular tunnel. In this topic, let’s learn about the volume of the half cylinder.
What is the volume of the half cylinder?
The volume of a half cylinder is the amount of space it occupies. It is calculated by using the formula: Volume = (π × radius² × height) / 2 Where ‘radius’ is the radius of the cylinder's base and ‘height’ is the height of the cylinder.
Volume of Half Cylinder Formula A half cylinder is derived from a full cylinder where one half is considered.
To calculate its volume, you find the volume of a full cylinder and then divide it by two. The formula for the volume of a half cylinder is given as follows: Volume = (π × r² × h) / 2
How to Derive the Volume of a Half Cylinder?
To derive the volume of a half cylinder, we use the concept of volume as the total space occupied by a 3D object.
Since a half cylinder is half of a full cylinder, its volume can be derived as follows:
The formula for the volume of a full cylinder is: Volume = π × radius² × height
For a half cylinder: Volume = (π × r² × h) / 2
How to find the volume of a half cylinder?
The volume of a half cylinder is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
Calculate the volume of the full cylinder first, and then divide it by two to find the volume of the half cylinder.
Let’s take a look at the formula for finding the volume of a half cylinder: Write down the formula Volume = (π × radius² × height) / 2
Once we know the radius and height, substitute those values into the formula to find the volume of the half cylinder.
Tips and Tricks for Calculating the Volume of Half Cylinder
Remember the formula: The formula for the volume of a half cylinder is straightforward: Volume = (π × radius² × height) / 2 Break it down: The volume is how much space fits inside the half cylinder.
You find the volume of a full cylinder and then divide by two. Simplify the numbers: If the radius and height are simple numbers, calculations become easier, e.g., if radius is 3 and height is 6, the volume is (π × 3² × 6) / 2 = 27π.
Check with full cylinder volume: If you are given the volume of a full cylinder, remember to halve it to find the volume of the half cylinder.
Common Mistakes and How to Avoid Them in Volume of Half Cylinder
Making mistakes while learning the volume of the half cylinder is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of half cylinders.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves different calculations, while volume is calculated by finding the space within. For a half cylinder, the volume formula is (π × r² × h) / 2.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the cylinder's perimeter instead of the volume formula. Volume is the space inside the shape, whereas perimeter refers to the total length around the edges of a 2D shape. Do not mix them up.
Mistake 3
Using the wrong formula for full cylinders
Some kids use the formula for the volume of a full cylinder (π × r² × h) instead of dividing it by two for the half cylinder.
Mistake 4
Confusing circular area with volume
Thinking of volume in terms of just the circular base area. This happens when someone uses only the circular base area instead of considering the height and the halving aspect for volume calculations.
Mistake 5
Incorrectly calculating the radius or height
Some students make errors in calculating or substituting the given radius or height. Ensure the values are accurate before using them in the formula.
Volume of Half Cylinder Examples
Problem 1
A half cylinder has a radius of 3 cm and a height of 6 cm. What is its volume?
The volume of the half cylinder is 27π cm³.
Explanation
To find the volume of a half cylinder, use the formula: V = (π × r² × h) / 2
Here, the radius is 3 cm and the height is 6 cm, so: V = (π × 3² × 6) / 2 = 27π cm³
Problem 2
A half cylinder has a radius of 5 m and a height of 10 m. Find its volume.
The volume of the half cylinder is 125π m³.
Explanation
To find the volume of a half cylinder, use the formula: V = (π × r² × h) / 2
Substitute the radius (5 m) and height (10 m): V = (π × 5² × 10) / 2 = 125π m³
Problem 3
The volume of a half cylinder is 50π cm³. If the height is 5 cm, what is the radius?
The radius of the half cylinder is 4 cm.
Explanation
If you know the volume of the half cylinder, and you need to find the radius, use the rearranged formula: Volume = (π × r² × h) / 2
100π = π × r² × 5 r² = 20 r = √20 = 4 cm
Problem 4
A half cylinder has a radius of 2.5 inches and a height of 8 inches. Find its volume.
The volume of the half cylinder is 25π inches³.
Explanation
Using the formula for volume: V = (π × r² × h) / 2
Substitute the radius 2.5 inches and height 8 inches: V = (π × 2.5² × 8) / 2 = 25π inches³
Problem 5
You have a half-cylinder-shaped tunnel with a radius of 4 feet and a height of 12 feet. How much space (in cubic feet) is available inside the tunnel?
The tunnel has a volume of 96π cubic feet.
Explanation
Using the formula for volume: V = (π × r² × h) / 2
Substitute the radius 4 feet and height 12 feet: V = (π × 4² × 12) / 2 = 96π ft³
FAQs on Volume of Half Cylinder
1.Is the volume of a half 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 or height be a decimal or fraction?
5.Is the volume of a half cylinder the same as the surface area?
Important Glossaries for Volume of Half Cylinder
- Radius: The distance from the center to the edge of the cylinder's circular base.
- Height: The distance between the two bases of the cylinder.
- Volume: The amount of space enclosed within a 3D object. For a half cylinder, the volume is calculated by halving the volume of a full cylinder.
- 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).
- π (Pi): A mathematical constant approximately equal to 3.14159, used in calculations involving circles.
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
