Volume of a Sphere Formula: How to Calculate & Examples

The volume of a sphere formula is V = 4/3 × π × r³, where r is the radius of the sphere. Volume is the amount of space inside the sphere, measured in cubic units (cm³, m³). π ≈ 3.14 or 22/7.

How to Calculate the Volume of a Sphere + Example

Steps:

1. Find the radius (r).
2. Cube the radius (r³).
3. Multiply: V = 4/3 × π × r³.

Worked Example: A sphere has a radius of 21 cm. What is its volume? (π = 22/7)

Solution: V = 4/3 × (22/7) × 21³ = 4/3 × (22/7) × 9,261 = 4/3 × 29,106 = 38,808 cm³

So the volume of the sphere is 38,808 cm³.

Why It Matters for Students

The volume of a sphere is part of the Curved Solids topic in Grade 9 and often appears in school and national exams. It helps children find the capacity of real objects such as a basketball, a globe, or a balloon.

Fun fact: A sphere's volume is exactly two thirds of the smallest cylinder that can contain it (a cylinder whose radius and height equal the sphere's diameter). Archimedes proved this relationship more than 2,000 years ago.

Also learn other solids: Volume of a Cylinder, Volume of a Cone, Volume of a Cube, and Volume of a Cuboid. See also Circumference of a Circle and all topics in the Mathematics hub.

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