Volume of a Cube Notes

Published on: September 29, 2026

This Volume of a Cube Calculator finds the space inside a cube from the length of one edge, and shows the working line by line. A cube measures the same along its length, its width and its height, so one edge describes the whole solid, and multiplying that edge by itself three times counts the unit cubes that fill it. The answer is written in cubic units. Following the same pattern every time is what makes the volume of a cube easy to check and repeat.

Cube labeled a

In the diagram, each edge is labeled \(a\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Work out the volume.

Formula:

\(V = a^{3}\)
See Example 1 Hide Example 1

Problem

\(a = 7\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Work out the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a cube whose edge length is \(a = 7\).

\(a = 7\)

Step 2

Step 2 - Write the formula.

In this problem: A cube has the same measurement along its length, its width and its height, so the volume is that edge length multiplied by itself three times.

\(V = a^{3}\)

Step 3

Step 3 - Substitute the edge length into the formula.

In this problem: Replacing \(a\) with \(7\) in \(V = a^{3}\) gives \(V = 7^{3}\).

\(V = 7^{3}\)

Step 4

Step 4 - Work out the volume.

In this problem: \(7^{3}\) means \(7 \times 7 \times 7\), and \(7 \times 7 \times 7 = 343\).

\(V = 7^{3} = 343\)

Final Answer

\(V = 343\)
See Example 2 Hide Example 2

Problem

\(a = 1.5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Work out the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a cube whose edge length is \(a = 1.5\).

\(a = 1.5\)

Step 2

Step 2 - Write the formula.

In this problem: A cube has the same measurement along its length, its width and its height, so the volume is that edge length multiplied by itself three times.

\(V = a^{3}\)

Step 3

Step 3 - Substitute the edge length into the formula.

In this problem: Replacing \(a\) with \(1.5\) in \(V = a^{3}\) gives \(V = 1.5^{3}\).

\(V = 1.5^{3}\)

Step 4

Step 4 - Work out the volume.

In this problem: \(1.5^{3}\) means \(1.5 \times 1.5 \times 1.5\), and \(1.5 \times 1.5 \times 1.5 \approx 3.38\).

\(V = 1.5^{3} \approx 3.38\)

Final Answer

\(V \approx 3.38\)
See Example 3 Hide Example 3

Problem

\(a = 5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Work out the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a cube whose edge length is \(a = 5\).

\(a = 5\)

Step 2

Step 2 - Write the formula.

In this problem: A cube has the same measurement along its length, its width and its height, so the volume is that edge length multiplied by itself three times.

\(V = a^{3}\)

Step 3

Step 3 - Substitute the edge length into the formula.

In this problem: Replacing \(a\) with \(5\) in \(V = a^{3}\) gives \(V = 5^{3}\).

\(V = 5^{3}\)

Step 4

Step 4 - Work out the volume.

In this problem: \(5^{3}\) means \(5 \times 5 \times 5\), and \(5 \times 5 \times 5 = 125\).

\(V = 5^{3} = 125\)

Final Answer

\(V = 125\)
See Example 4 Hide Example 4

Problem

\(a = 2.5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Work out the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a cube whose edge length is \(a = 2.5\).

\(a = 2.5\)

Step 2

Step 2 - Write the formula.

In this problem: A cube has the same measurement along its length, its width and its height, so the volume is that edge length multiplied by itself three times.

\(V = a^{3}\)

Step 3

Step 3 - Substitute the edge length into the formula.

In this problem: Replacing \(a\) with \(2.5\) in \(V = a^{3}\) gives \(V = 2.5^{3}\).

\(V = 2.5^{3}\)

Step 4

Step 4 - Work out the volume.

In this problem: \(2.5^{3}\) means \(2.5 \times 2.5 \times 2.5\), and \(2.5 \times 2.5 \times 2.5 \approx 15.62\).

\(V = 2.5^{3} \approx 15.62\)

Final Answer

\(V \approx 15.62\)