Class 9 - Volume of Sphere | Definition, Formula & Example

The volume of a sphere tells us how much space is enclosed within a perfectly round 3D object. From sports balls to planets, spheres are everywhere, and calculating their volume is essential in both academic and real-world contexts. In this guide, you'll explore the volume of a sphere formula, its step-by-step derivation, and real-life examples to help you understand and apply the concept easily.

Table of Contents

• What is the Volume of a Sphere
• Formula for Volume of a Sphere
• How to Calculate Volume of a Sphere
• Solved Examples on Volume of a Sphere

What is the Volume of a Sphere

The volume of a sphere is a measure of the three-dimensional space enclosed within a sphere. A sphere is a perfectly symmetrical 3D shape, where every point on the surface is equidistant from its center. The volume of sphere essentially tells us how much space is contained inside the sphere.

Volume of Sphere Formula

The standard volume of sphere formula is:
Volume of Sphere = (4/3) × π × r³
Where r is the radius of the sphere and π ≈ 3.14159

This formula calculates the sphere volume in cubic units, based on the radius of sphere.

How to Calculate the Volume of Sphere 

To calculate the volume of sphere, you need either the radius of sphere or the diameter of the sphere.

1. Using Radius of Sphere: When the radius of sphere is given, we can directly use it in the formula to evaluate the volume of a sphere:
   V = (4/3) π r³

2. Using Diameter of Sphere: When the diameter of sphere d (r = d/2) is given we can calculate the volume of sphere using formula:
   V = (4/3) π (d/2)³ = (π d³) / 6
   

Solved Examples on Volume of Sphere

Let’s go through a few sphere volume examples to understand how to apply the formula:

Example 1: What will be the volume of sphere with a radius = 3 cm.
Solution: V = (4/3) π (3)³ = (4/3) π (27) = 36π ≈ 113.1 cm³

Example 2: Find the volume of sphere with a diameter of sphere = 10 cm.
Solution: r = 10/2 = 5 cm
V = (4/3) π (5)³ = (4/3) π (125) = (500/3) π ≈ 523.6 cm³

Example 3: A ball has a surface area of sphere = 314.16 cm². Find the volume of sphere.
Solution: First, find the radius of sphere:
4π r² = 314.16 → r² = 314.16 / (4π) = 25 → r = 5
V = (4/3) π (5)³ = (500/3) π ≈ 523.6 cm³