100 LearnersLast updated on July 17th, 2025
Volume of Sphere
The volume of a sphere is the total space it occupies or the number of cubic units it can hold. A sphere is a 3D shape where every point on its surface is equidistant from its center. To find the volume of a sphere, we use the formula involving its radius. In real life, kids relate to the volume of a sphere by thinking of things like a basketball, a marble, or a globe. In this topic, let’s learn about the volume of a sphere.
What is the volume of the sphere?
The volume of a sphere is the amount of space it occupies. It is calculated by using the formula: Volume = (4/3)πr³ Where ‘r’ is the radius of the sphere.
Volume of Sphere Formula A sphere is a 3-dimensional shape where all points on its surface are equidistant from its center.
To calculate its volume, you use the radius of the sphere.
The formula for the volume of a sphere is as follows: Volume = (4/3)πr³
How to Derive the Volume of a Sphere?
To derive the volume of a sphere, we use the concept of volume as the total space occupied by a 3D object.
The formula for the volume of a sphere can be derived using integral calculus, but it is commonly presented as:
Volume = (4/3)πr³ Where ‘r’ is the radius of the sphere.
How to find the volume of a sphere?
The volume of a sphere is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
To find the volume, cube the radius, multiply it by π, and then multiply by 4/3.
Here’s the formula for finding the volume of a sphere: Write down the formula: Volume = (4/3)πr³ The radius is the distance from the center of the sphere to any point on its surface.
Once you know the radius, substitute that value for ‘r’ in the formula Volume = (4/3)πr³
Tips and Tricks for Calculating the Volume of Sphere
Remember the formula: The formula for the volume of a sphere is: Volume = (4/3)πr³ Break it down: The volume is how much space fits inside the sphere.
Simplify calculations: If the radius is a simple number, use that to quickly compute the volume.
Estimate using π: You can use 3.14 or 22/7 as an approximation for π for easier calculations.
Common Mistakes and How to Avoid Them in Volume of Sphere
Making mistakes while learning the volume of the sphere is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of spheres.
Volume of Sphere Examples
Problem 1
A sphere has a radius of 3 cm. What is its volume?
The volume of the sphere is approximately 113.1 cm³.
Explanation
To find the volume of a sphere, use the formula: V = (4/3)πr³ Here, the radius is 3 cm, so: V = (4/3)π(3)³ ≈ 113.1 cm³
Problem 2
A basketball has a radius of 5 inches. Find its volume.
The volume of the basketball is approximately 523.6 inches³.
Explanation
To find the volume of a sphere, use the formula: V = (4/3)πr³ Substitute the radius (5 inches): V = (4/3)π(5)³ ≈ 523.6 inches³
Problem 3
The volume of a sphere is 904.32 m³. What is the radius of the sphere?
The radius of the sphere is approximately 6 m.
Explanation
If you know the volume of the sphere and need to find the radius, solve for r in the formula: V = (4/3)πr³ 904.32 = (4/3)πr³ r ≈ 6 m
Problem 4
A marble has a radius of 1 cm. Find its volume.
The volume of the marble is approximately 4.19 cm³.
Explanation
Using the formula for volume: V = (4/3)πr³ Substitute the radius 1 cm: V = (4/3)π(1)³ ≈ 4.19 cm³
Problem 5
You have a globe with a radius of 10 cm. How much space (in cubic centimeters) does it occupy?
The globe has a volume of approximately 4188.79 cm³.
Explanation
Using the formula for volume: V = (4/3)πr³ Substitute the radius 10 cm: V = (4/3)π(10)³ ≈ 4188.79 cm³
FAQs on Volume of Sphere
1.Is the volume of a 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 sphere the same as its surface area?
Important Glossaries for Volume of Sphere
- Radius: The distance from the center of the sphere to any point on its surface.
- Volume: The amount of space enclosed within a 3D object. For a sphere, it is calculated using the formula (4/3)πr³.
- π (Pi): A mathematical constant approximately equal to 3.14159, used in calculations involving circles and spheres.
- Cubic Units: The units of measurement used for volume. If the radius is in centimeters (cm), the volume will be cubic centimeters (cm³), if in meters, it will be in cubic meters (m³).
- Sphere: A 3D shape where every point on its surface is equidistant from its center.
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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
