101 LearnersLast updated on July 17th, 2025
Volume of Hemisphere
The volume of a hemisphere is the amount of space it occupies or the number of cubic units it can hold. A hemisphere is a 3D shape that represents half of a sphere. To find the volume of a hemisphere, we use the formula that involves pi and the radius of the sphere. In real life, kids can relate to the volume of a hemisphere by thinking of things like half a ball or a dome. In this topic, let’s learn about the volume of a hemisphere.
What is the volume of the hemisphere?
The volume of a hemisphere is the amount of space it occupies.
It is calculated using the formula: Volume = (2/3)πr³ Where ‘r’ is the radius of the sphere from which the hemisphere is derived.
The formula for the volume of a hemisphere is derived from that of a full sphere, which is (4/3)πr³.
Since a hemisphere is half of a sphere, its volume is half of that, which is (2/3)πr³.
How to Derive the Volume of a Hemisphere?
To derive the volume of a hemisphere, we start with the concept of the volume of a full sphere.
The formula for the volume of a sphere is: Volume = (4/3)πr³
Since a hemisphere is half of a sphere, we divide this volume by 2: Volume of Hemisphere = (1/2) x (4/3)πr³ = (2/3)πr³
How to find the volume of a hemisphere?
The volume of a hemisphere is always expressed in cubic units, for example, cubic centimeters cm³, cubic meters m³.
First, determine the radius of the sphere, and then use the formula to calculate the volume.
Let’s take a look at the formula for finding the volume of a hemisphere:
Write down the formula: Volume = (2/3)πr³ Once we know the radius, substitute that value for ‘r’ in the formula to find the volume.
Tips and Tricks for Calculating the Volume of Hemisphere
Remember the formula: The formula for the volume of a hemisphere is: Volume = (2/3)πr³ Break it down:
The volume is how much space fits inside the half-sphere.
Multiply by (2/3) to account for the hemisphere. Simplify the numbers: If the radius is a simple number like 2, 3, or 4, it is easy to cube and then multiply by (2/3)π.
For example, if r = 3, V = (2/3)π(3³).
Check for cube roots If you are given the volume and need to find the radius, you can solve for the cube root after rearranging the formula.
Common Mistakes and How to Avoid Them in Volume of Hemisphere
Making mistakes while learning the volume of the hemisphere is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of hemispheres.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area.
Surface area involves both the curved surface and the base of the hemisphere, while volume is calculated using (2/3)πr³.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the hemisphere’s perimeter instead of the volume formula.
Volume is the space inside the hemisphere, whereas perimeter refers to the total length around the base of a 2D shape. Do not mix them up.
Mistake 3
Using the wrong Formula for Spheres
Some kids use the formula for the volume of a full sphere ((4/3)πr³) instead of the hemisphere formula ((2/3)πr³).
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 without solving for the radius correctly.
For example, if the volume is given, and they need to find the radius, they might forget to take the cube root after rearranging the formula.
Volume of Hemisphere Examples
Problem 1
A hemisphere has a radius of 4 cm. What is its volume?
The volume of the hemisphere is approximately 134.04 cm³.
Explanation
To find the volume of a hemisphere, use the formula: V = (2/3)πr³ Here, the radius is 4 cm, so: V = (2/3)π(4³) ≈ 134.04 cm³
Problem 2
A hemisphere has a radius of 10 m. Find its volume.
The volume of the hemisphere is approximately 2094.40 m³.
Explanation
To find the volume of a hemisphere, use the formula: V = (2/3)πr³ Substitute the radius (10 m): V = (2/3)π(10³) ≈ 2094.40 m³
Problem 3
The volume of a hemisphere is 500 cm³. What is the radius of the hemisphere?
The radius of the hemisphere is approximately 5.42 cm.
Explanation
If you know the volume of the hemisphere, and you need to find the radius, you’ll rearrange the formula and solve: V = (2/3)πr³ 500 = (2/3)πr³ r³ ≈ 238.73 r ≈ 5.42 cm
Problem 4
A hemisphere has a radius of 2.5 inches. Find its volume.
The volume of the hemisphere 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(2.5³) ≈ 32.72 inches³
Problem 5
You have a dome-shaped bowl with a radius of 3 feet. How much space (in cubic feet) is available inside the bowl?
The bowl 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(3³) ≈ 56.55 ft³
FAQs on Volume of Hemisphere
1.Is the volume of a hemisphere 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.Does the formula for the volume of a hemisphere include the base?
Important Glossaries for Volume of Hemisphere
- Radius: The distance from the center to the edge of the hemisphere. It's crucial for calculating volume.
- Volume: The amount of space enclosed within a 3D object. For a hemisphere, it is calculated using (2/3)πr³.
- Cubic units: The units of measurement for volume. If the radius is in centimeters (cm), the volume is in cubic centimeters (cm³).
- Pi (π): A mathematical constant approximately equal to 3.14159, used in calculations involving circles and spheres.
- Hemisphere: A 3D shape representing half of a sphere, crucial for understanding its volume calculations.
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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
