Volume of a Hemisphere: Definition, Formula, and Solved Examples
Chandni 30 Jun, 2025
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Volume of a Hemisphere: Hemispheres are not just abstract geometric shapes; they’re all around us! From the curved dome of an igloo to the smooth shape of a bowl, hemispheres play a role in our everyday lives.
Have you ever wondered how much space these shapes occupy? Understanding the volume of a hemisphere isn’t just about math; it is useful in design, architecture, and calculating the capacity of objects like tanks or molds. In this blog, we will learn how to calculate the volume of a hemisphere with stepwise solved examples.What is Hemisphere?
A hemisphere is a three-dimensional shape that results from cutting a sphere into two equal halves along its diameter. The term "hemi" means "half," and "sphere" refers to the round, ball-like 3D shape. Thus, a hemisphere is literally half of a sphere. It consists of a curved, half-spherical surface that forms the outer part of the shape and a flat circular base that forms the bottom of the shape when placed on a flat surface. Hemispheres are seen in nature and everyday life, such as :- Northern Hemisphere and Southern Hemisphere of Earth
- Igloo structures in polar regions
- The upper half of a tennis ball
- Bowls in the kitchen
- Domes in architecture
All of these shapes can help us understand what is the volume of a hemisphere in practical, real-life situations.
Volume of Hemisphere Definition
The volume of a hemisphere represents the amount of space it occupies or the capacity it can hold. For example, it helps determine how much liquid a hemispherical bowl can contain, the space inside a dome-shaped structure, or the material needed to create half of a sphere. The volume is measured in cubic units, such as cm 3 , m 3 or in 3 , to quantify this space accurately.Volume of Hemisphere Formula
A hemisphere is essentially half of a sphere, which means its volume will also be half of the sphere's volume.The formula to calculate volume of a sphere is 4/3πr 3
Since the hemisphere is half of the sphere, its volume can be calculated as 1/2× 4/3πr 3 Simplifying this, the formula for the volume of a hemisphere becomes 2 /3πr 3A hemisphere is essentially half of a sphere, which means its volume will also be half of the sphere's volume.
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The formula to calculate the volume of a sphere is:
4/3 × π × r³ -
Since a hemisphere is half of a sphere, its volume can be calculated as:
1/2 × 4/3 × π × r³ = 2/3 × π × r³
This is known as the hemisphere volume formula. It’s simple and easy to remember.
Read More - 3D Shapes - Definition, Properties, Types and Formulas
Volume of Hemisphere Derivation
The volume of the hemisphere is two-thirds of the product of π and the cube of its radius. The volume of a sphere is experimentally proven to be two-thirds of the volume of a cylinder that has the same radius and a height equal to the diameter of the sphere.
To begin, consider the volume of such a cylinder. For a cylinder with radius r and height equal to 2r (the sphere's diameter), the volume is calculated as:
Volume of Cylinder = πr 2 × (2r) = 2πr 3
From this relationship, the volume of the sphere is two-thirds of the cylinder's volume: 2/3 × 2πr 3 = 4/3πr 3 Now, since a hemisphere is half of a sphere, its volume is simply half the volume of the sphere. Dividing the sphere's volume by 2 gives: 4/3πr 3 /2 = 2/3πr 3Thus, the formula for the volume of a hemisphere is derived as 2/3πr 3
Here, r represents the radius of the hemisphere, and the formula calculates the three-dimensional space it occupies.Using a Hemisphere Volume Calculator
Want to check your answer quickly? Use a hemisphere volume calculator online! All you need to enter is the radius, and the calculator will use the formula 2/3πr³ to give you the answer instantly. This helps when checking homework or solving tricky problems quickly.
So next time someone asks, “what is the volume of a hemisphere?”, just pull up a calculator and impress them with your skills.
Understanding the volume of hemisphere is not only important for math exams, but it also has real-life applications. From simple formulas like the hemisphere volume formula to fun activities and calculators, this topic can actually be quite exciting!
So next time you see a bowl, a dome, or even a globe—ask yourself:
“What is the volume of a hemisphere like this?”
You’ll know exactly how to find out!
Read More - Surface Area Formulas: Definitions, Derivations, and Examples
Volume of Hemisphere Solved Examples
Example 1: Find the volume of a hemisphere with a radius of 10 cm. Solution: Step 1: The radius (r) of the hemisphere is 10 cm. Step 2: Use the formula for the volume of a hemisphere: Volume of Hemisphere = 2/3πr³ Step 3 : Substitute r = 10 and π = 3.14 Volume of Hemisphere= 2/3 × 3.14 × (10) 3 Step 4 : Calculate: Volume of Hemisphere = 2/3 × 3.14 × 1000 The volume of the hemisphere is approximately 2093.33 cm³.- Length (l) = 2r = 2 × 4 = 8 cm
- Breadth (b) = 2r = 8 cm
- Height (h) = r = 4 cm
Example 5: If the volume of a hemisphere is 5.236 m ³ , find the radius of the hemisphere.
Solution :
The formula for the volume of a hemisphere is 2/3πr³ We are given a volume of hemisphere, i.e., 5.236 m ³. Substituting this value into the formula: 5.236 = 2/3πr³ Multiply by 3/2 πr ³ = 7.854 Divide by π r ³ = 7.854/3.1416 ≈ 2.5 Take cube root: r = ∛ 2.5 ≈ 1.357 m| Related Articles | |
| Area of Rectangle | Isosceles Triangle |
| Composite Numbers | Triangle |
| Perimeter of Rectangle | Surface Area of Cylinder |
Volume of Hemisphere FAQs
Can a hemisphere have a negative volume?
What is the significance of π\piπ in the formula?
Can the formula be used for irregular shapes?
What is the relationship between the volume and surface area of a hemisphere?
How does the volume change if the radius is halved?
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