Volume of Sphere
2026-02-28 11:25 Diff
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Last updated on August 5, 2025

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

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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.

Problem 1

A sphere has a radius of 3 cm. What is its volume?

Okay, lets begin

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

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Problem 2

A basketball has a radius of 5 inches. Find its volume.

Okay, lets begin

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

Well explained 👍

Problem 3

The volume of a sphere is 904.32 m³. What is the radius of the sphere?

Okay, lets begin

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

Well explained 👍

Problem 4

A marble has a radius of 1 cm. Find its volume.

Okay, lets begin

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

Well explained 👍

Problem 5

You have a globe with a radius of 10 cm. How much space (in cubic centimeters) does it occupy?

Okay, lets begin

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

Well explained 👍

FAQs on Volume of Sphere

1.Is the volume of a sphere the same as the surface area?

No, the volume and surface area of a sphere are different concepts: Volume refers to the space inside the sphere and is given by V = (4/3)πr³.

Surface area is the total area of the sphere's surface and is given by A = 4πr².

2.How do you find the volume if the radius is given?

To calculate the volume when the radius is provided, cube the radius, multiply by π, and then multiply by 4/3. For example, if the radius is 4 cm, the volume would be: V = (4/3)π(4)³.

3.What if I have the volume and need to find the radius?

If the volume of the sphere is given and you need to find the radius, rearrange the formula to solve for r: V = (4/3)πr³ Then take the cube root after dividing by (4/3)π.

4.Can the radius be a decimal or fraction?

Yes, the radius of a sphere can be a decimal or fraction. For example, if the radius is 2.5 inches, the volume would be: V = (4/3)π(2.5)³.

5.Is the volume of a sphere the same as its surface area?

No, the volume and surface area of a sphere are different concepts: Volume refers to the space inside the sphere and is given by V = (4/3)πr³.

Surface area refers to the total area of the sphere’s surface.

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