102 LearnersLast updated on 5 September 2025
Volume of Half Sphere
The volume of a half sphere is the total space it occupies or the number of cubic units it can hold. A half sphere is a 3D shape that results from slicing a sphere into two equal parts. To find the volume of a half sphere, we calculate half of the sphere's volume using its radius. In real life, kids relate to the volume of a half sphere by thinking of things like a dome or half of a ball. In this topic, let’s learn about the volume of a half sphere.
What is the volume of the half sphere?
The volume of a half sphere is the amount of space it occupies. It is calculated by using the formula:
Volume = (2/3)πr³ Where ‘r’ is the radius of the sphere.
Volume of Half Sphere Formula A half sphere is a 3-dimensional shape that is half of a full sphere.
To calculate its volume, you multiply the volume of a full sphere by 1/2. The formula for the volume of a half sphere is given as follows:
Volume = (2/3)πr³
How to Derive the Volume of a Half Sphere?
To derive the volume of a half sphere, we use the concept of volume as the total space occupied by a 3D object. Since a half sphere is half of a full sphere, its volume can be derived as follows:
The formula for the volume of a full sphere is: Volume = (4/3)πr³
For a half sphere, we take half of this volume: Volume = (1/2) x (4/3)πr³
Volume = (2/3)πr³
How to find the volume of a half sphere?
The volume of a half sphere is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). Calculate the volume of the full sphere and then divide it by 2 to find the volume of the half sphere. Let’s take a look at the formula for finding the volume of a half sphere:
Write down the formula Volume = (2/3)πr³ The radius is the distance from the center to the edge of the sphere.
The radius is the only measurement needed to calculate the volume because the formula is based on the radius.
Once we know the radius, substitute that value for ‘r’ in the formula Volume = (2/3)πr³
To find the volume, calculate (2/3)π times the radius cubed.
Tips and Tricks for Calculating the Volume of Half Sphere
Remember the formula: The formula for the volume of a half sphere is simple: Volume = (2/3)πr³
Break it down: The volume is how much space fits inside the half sphere.
Simplify the numbers: If the radius is a simple number, it is easy to compute, for example, if r = 3, then (2/3)π(3)³ = 18π.
Check for cube roots: If you are given the volume and need to find the radius, you can find the cube root of the volume after multiplying by 3/2π.
Common Mistakes and How to Avoid Them in Volume of Half Sphere
Making mistakes while learning the volume of the half sphere is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of half spheres.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. The surface area of a half sphere includes the curved surface and the flat circular base, while the volume is calculated as (2/3)πr³.
Mistake 2
Confusing Volume with Diameter
Some kids may think of the sphere’s diameter instead of the radius for the volume formula. Volume is calculated using the radius, not the diameter.
Mistake 3
Using the wrong Formula for Cylinders
Some kids use the formula for the volume of a cylinder instead of the half sphere formula.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements. This happens when someone uses the radius (which is a linear measurement) instead of understanding that volume relates to cubic measurements.
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 take the cube root of the volume after adjusting for (2/3)π.
Volume of Half Sphere Examples
Problem 1
A half sphere has a radius of 4cm. What is its volume?
The volume of the half sphere is approximately 134.04 cm³.
Explanation
To find the volume of a half sphere, use the formula: V = (2/3)πr³
Here, the radius is 4 cm, so: V = (2/3)π(4)³ ≈ 134.04 cm³
Problem 2
A half sphere has a radius of 10 m. Find its volume.
The volume of the half sphere is approximately 2094.4 m³.
Explanation
To find the volume of a half sphere, use the formula: V = (2/3)πr³
Substitute the radius (10 m): V = (2/3)π(10)³ ≈ 2094.4 m³
Problem 3
The volume of a half sphere is 500 cm³. What is the radius of the sphere?
The radius of the sphere is approximately 5.42 cm.
Explanation
If you know the volume of the half sphere, and you need to find the radius, adjust for (2/3)π and take the cube root.
500 = (2/3)πr³ r³ = (500 x 3)/(2π) r ≈ 5.42 cm
Problem 4
A half sphere has a radius of 2.5 inches. Find its volume.
The volume of the half sphere is approximately 32.72 inches³.
Explanation
Using the formula for volume: V = (2/3)πr³
Substitute the radius 2.5 inches: V = (2/3)π(2.5)³ ≈ 32.72 inches³
Problem 5
You have a half-sphere shaped dome with a radius of 3 feet. How much space (in cubic feet) is available inside the dome?
The dome has a volume of approximately 56.55 cubic feet.
Explanation
Using the formula for volume: V = (2/3)πr³
Substitute the radius 3 feet: V = (2/3)π(3)³ ≈ 56.55 ft³
FAQs on Volume of Half Sphere
1.Is the volume of a half sphere the same as the surface area?
2.How do you find the volume if the radius is 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 half sphere the same as that of a full sphere?
Important Glossaries for Volume of Half Sphere
- Radius: The distance from the center to the edge of the sphere. It's the only measurement needed for volume calculations.
- Volume: The amount of space enclosed within a 3D object. For a half sphere, it is calculated by (2/3)πr³.
- Cubic units: The units of measurement used for volume. If the radius is in centimeters (cm), the volume will be in cubic centimeters (cm³).
- Sphere: A 3D object where every point on the surface is equidistant from the center.
- Half Sphere: A 3D shape derived from cutting a sphere into two equal parts, having both a curved surface and a flat circular base.
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
