Volume of a Sphere Calculator

Published on: September 1, 2024

Final Answer: Free • Full Steps: Plus

This Volume of a Sphere Calculator helps you find the space inside a sphere when the radius is known. It uses the formula V = 4/3 × π × r³, where r is the radius and the answer is written in cubic units. First cube the radius, then multiply by 4/3 × π to get the volume. It is a simple way to check answers, understand the sphere volume formula, and practise basic geometry step by step.

In the diagram, the radius is labeled r.

Step-by-step method

Identify what is given.
Write the formula.
Substitute the value and calculate the volume.

Formula:

\(V = \frac{4}{3}\pi r^{3}\)

Example 1:

\(r = 5\)

Step 1 - Identify what is given.

In this problem: The given radius is \(r = 5\).

\(r = 5\)

Step 2 - Write the formula.

In this problem: Use the sphere volume formula: \(V = \frac{4}{3}\pi r^{3}\).

\(V = \frac{4}{3}\pi r^{3}\)

Step 3 - Substitute the value and calculate the volume.

In this problem: Substitute \(r = 5\): \(V = \frac{4}{3}\pi \times 5^{3} \approx 523.6\).

\(V = \frac{4}{3}\pi \times 5^{3} \approx 523.6\)

Final answer:

\(V \approx 523.6\)

Example 2:

\(r = 2.5\)

Step 1 - Identify what is given.

In this problem: The given radius is \(r = 2.5\).

\(r = 2.5\)

Step 2 - Write the formula.

In this problem: Use the sphere volume formula: \(V = \frac{4}{3}\pi r^{3}\).

\(V = \frac{4}{3}\pi r^{3}\)

Step 3 - Substitute the value and calculate the volume.

In this problem: Substitute \(r = 2.5\): \(V = \frac{4}{3}\pi \times 2.5^{3} \approx 65.45\).

\(V = \frac{4}{3}\pi \times 2.5^{3} \approx 65.45\)

Final answer:

\(V \approx 65.45\)