106 LearnersLast updated on July 9th, 2025
Volume of Sphere with Diameter
The volume of a sphere is the amount of space it occupies, measured in cubic units. A sphere is a perfectly round 3D shape with every point on its surface equidistant from its center. The volume of a sphere can be calculated if you know its diameter or radius. In this topic, let’s learn about the volume of a sphere, specifically when given the diameter.
What is the volume of the sphere with diameter?
The volume of a sphere is the amount of space it occupies. It is calculated using the formula: Volume = (4/3)πr³ Where ‘r’ is the radius of the sphere. Given the diameter, the radius is half the diameter.
Volume of Sphere Formula To find the volume of a sphere, you need to know its radius. You can derive the radius from the diameter by dividing the diameter by 2.
The formula for the volume of a sphere is: 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 volume is derived from integrating the areas of infinitesimally small disks that make up the sphere.
The formula for the volume of a sphere is: Volume = (4/3)πr³
If given the diameter: Radius = Diameter / 2 Volume = (4/3)π(Diameter/2)³
How to find the volume of a sphere?
The volume of a sphere is always expressed in cubic units, for example, cubic centimeters (cm³) or cubic meters (m³). To find the volume, use the radius, which is half of the diameter.
Use the formula: Volume = (4/3)πr³ Where r is the radius (half of the diameter).
This is the only measurement needed to calculate the volume. Once you know the radius, substitute that value into the formula to find the volume.
Tips and Tricks for Calculating the Volume of a 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. You just need to know the radius, which is half of the diameter.
- Simplify the numbers: If the diameter is a simple number, it’s easy to calculate the radius and then cube it.
- Check for cube roots: If you are given the volume and need to find the radius, you can find the cube root after dividing by (4/3)π.
Common Mistakes and How to Avoid Them in Volume of Sphere
Making mistakes while learning the volume of a 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.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area is calculated by 4πr², but volume is calculated by (4/3)πr³. For example, volume is not 4πr².
Mistake 2
Confusing Volume with Circumference
Some kids may think of the sphere’s circumference instead of the volume formula. Volume is the space inside the sphere, whereas circumference refers to the distance around the sphere.
Mistake 3
Using the wrong formula for cylinders
Some kids use the formula for the volume of a cylinder (πr²h) instead of the sphere formula.
Mistake 4
Confusing cubic volume with linear measurements
Thinking of volume in terms of linear measurements. This happens when someone uses the diameter or radius directly without cubing it to understand that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the radius
Some students calculate the given volume without correctly finding the radius from the diameter. For example, they might forget to divide the diameter by 2 to find the radius.
Volume of Sphere Examples
Problem 1
A sphere has a diameter of 6 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 diameter is 6 cm, so the radius is 3 cm: V = (4/3)π(3)³ ≈ 113.1 cm³
Problem 2
A sphere has a diameter of 12 m. Find its volume.
The volume of the sphere is approximately 904.8 m³.
Explanation
To find the volume of a sphere, use the formula: V = (4/3)πr³
Substitute the diameter (12 m) to find the radius (6 m): V = (4/3)π(6)³ ≈ 904.8 m³
Problem 3
The volume of a sphere is 268 cm³. What is the diameter of the sphere?
The diameter of the sphere is approximately 8.2 cm.
Explanation
If you know the volume of the sphere and need to find the diameter,
find the radius first by solving: (4/3)πr³ = 268 r ≈ 4.1 cm, so the diameter is 2 x 4.1 ≈ 8.2 cm
Problem 4
A sphere has a diameter of 5 inches. Find its volume.
The volume of the sphere is approximately 65.4 inches³.
Explanation
Using the formula for volume: V = (4/3)πr³
Substitute the diameter (5 inches) to find the radius (2.5 inches): V = (4/3)π(2.5)³ ≈ 65.4 inches³
Problem 5
You have a spherical ball with a diameter of 10 feet. How much space (in cubic feet) does it occupy?
The ball has a volume of approximately 523.6 cubic feet.
Explanation
Using the formula for volume: V = (4/3)πr³
Substitute the diameter (10 feet) to find the radius (5 feet): V = (4/3)π(5)³ ≈ 523.6 ft³
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 diameter is given?
3.What if I have the volume and need to find the diameter?
4.Can the diameter be a decimal or fraction?
5.Is the volume of a sphere the same as the surface area?
Important Glossaries for Volume of Sphere
- Diameter: The length of a straight line passing through the center of the sphere, connecting two points on its surface.
- Radius: Half of the diameter; 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 by the formula (4/3)πr³, expressed in cubic units.
- Cubic Units: The units of measurement used for volume. If the radius is in centimeters (cm), the volume will be in cubic centimeters (cm³), if in meters, it will be in cubic meters (m³).
- Surface Area: The total area of the sphere’s surface, calculated with the formula 4πr².
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
