Volume of Circle
2026-02-28 11:53 Diff
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Last updated on August 5, 2025

The volume of a circle is a concept that extends beyond the usual understanding of a 2D shape to a 3D space. However, in reality, a circle itself is only a 2-dimensional shape, so it does not have volume. Instead, when thinking about volume related to circles, we consider the volume of a sphere, which is a 3D object where all points are equidistant from the center. In this topic, let’s learn about the volume related to circles, specifically focusing on spheres.

How to Derive the Volume of a Sphere?

To derive the volume of a sphere, we start with the concept of volume as the total space occupied by a 3D object.

The formula for the volume of a sphere is:

Volume = (4/3) × π × r³

This formula:

  • Uses r, the radius of the sphere.

  • Includes π to account for the circular symmetry of the sphere.

  • Incorporates the factor 4/3, which arises from the integration process used in calculus to sum up the infinite thin circular disks that form the sphere.

Although this formula is rooted in integral calculus, it can also be appreciated conceptually as a way to measure how much space is inside a perfectly round 3D shape.

How to find the volume of a sphere?

The volume of a sphere is always expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

To find the volume, follow these steps:

  1. Measure the radius of the sphere.

  2. Use the formula:
    Volume = (4/3) × π × r³

  3. Substitute the radius value into the formula and perform the calculations.

This will give you the volume of the sphere in cubic units, representing the 3D space it occupies.

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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) × π × r³

Break it down:

  • The volume is the amount of space inside the sphere.

  • The radius is the key measurement used to calculate that space.

Simplify the numbers:

  • If the radius is a simple number like 2, 3, or 4, it's easier to cube it and calculate the volume.

Check for sphere roots:

  • If you're given the volume and need to find the radius, rearrange the formula and take the cube root to solve backward.

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.

Problem 1

A sphere has a radius of 4 cm. What is its volume?

Okay, lets begin

The volume of the sphere is approximately 268.08 cm³.

Explanation

To find the volume of a sphere, use the formula: V = \( \frac{4}{3} \pi r^3 \) Here, the radius is 4 cm, so: V = \( \frac{4}{3} \pi (4)^3 \approx 268.08 \) cm³

Well explained 👍

Problem 2

A sphere has a radius of 10 m. Find its volume.

Okay, lets begin

The volume of the sphere is approximately 4188.79 m³.

Explanation

To find the volume of a sphere, use the formula: V = \( \frac{4}{3} \pi r^3 \) Substitute the radius (10 m): V = \( \frac{4}{3} \pi (10)^3 \approx 4188.79 \) m³

Well explained 👍

Problem 3

The volume of a sphere is 904.78 cm³. What is the radius of the sphere?

Okay, lets begin

The radius of the sphere is approximately 6 cm.

Explanation

If you know the volume of the sphere and need to find the radius, take the cube root of the volume divided by 43π\frac{4}{3}\pi34​π.

The formula is:
r = ∛( V / ((4/3)π) )

This rearranged version of the volume formula helps you solve for r when V is known.

Well explained 👍

Problem 4

A sphere has a radius of 2.5 inches. Find its volume.

Okay, lets begin

The volume of the sphere is approximately 65.45 inches³.

Explanation

Using the formula for volume:
V = (4/3) × π × r³

Step 1: Substitute the radius 2.5 inches:
V = (4/3) × π × (2.5)³
V = (4/3) × π × 15.625
V ≈ (4/3) × 3.1416 × 15.625
V ≈ 65.45 inches³

Therefore, the volume of the sphere is approximately 65.45 cubic inches.

Well explained 👍

Problem 5

You have a spherical water balloon with a radius of 3 feet. How much space (in cubic feet) does it occupy?

Okay, lets begin

The balloon has a volume of approximately 113.10 cubic feet.

Explanation

Using the formula for volume:
V = (4/3) × π × r³

Step 1: Substitute the radius 3 feet:
V = (4/3) × π × (3)³
V = (4/3) × π × 27
V ≈ (4/3) × 3.1416 × 27
V ≈ 113.10 ft³

Therefore, the volume of the sphere is approximately 113.10 cubic feet.

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 calculated by:
    V = (4/3) × π × r³

  • Surface area refers to the total area of the sphere's outer surface and is calculated by:
    A = 4 × π × r²

So, while both formulas use π and the radius, volume involves r³ (cubic units) and surface area involves r² (square units).

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

To calculate the volume when the radius is provided, use the formula:
V = (4/3) × π × r³

Example:
If the radius is 4 cm:
V = (4/3) × π × (4)³
V = (4/3) × π × 64
V ≈ (4/3) × 3.1416 × 64
V ≈ 268.08 cm³

Therefore, the volume of the sphere is approximately 268.08 cubic centimeters.

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, take the cube root of the volume divided by

r = ∛(3V / (4π))

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 × r³
V = (4/3) × π × (2.5)³ ≈ 65.45 in³

5.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=34​πr3

Important Glossaries for Volume of Sphere

  • Radius: The distance from the center of the sphere to any point on its surface. It is essential for calculating both volume and surface area.

  • Volume: The amount of space enclosed within a 3D object.
    Formula for a sphere:
    V=43πr3V = \frac{4}{3} \pi r^3V=34​πr3

  • Sphere: A 3-dimensional shape where all points on the surface are equidistant from the center — like a basketball or a globe.

  • Cubic Units: Units used to measure volume.

    • If the radius is in centimeters (cm) → volume is in cubic centimeters (cm³).

    • If in meters (m) → volume is in cubic meters (m³).

  • Pi (π): A mathematical constant used in geometry, approximately equal to 3.14159, and common in formulas involving circles and spheres.

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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