How to Calculate the Volume of a Cube: Formula & Practice

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• 0:22 Definition of Volume
• 1:33 Calculating Volume
• 3:09 Examples
• 4:35 Lesson Summary

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Lesson Transcript
Instructor: Greg Williamson

Greg teaches both K-12 and college level math classes.

In this lesson, you will explore the formula used to calculate the volume of a cube. You will also gain a conceptual understanding of volume and appropriate units to use. Then test your knowledge in a brief quiz.

Definition of Volume

What do children's blocks, a milk crate, and dice have in common?

What is unique about the shape of the sides?

Each of these objects is an example of a perfect cube. A cube is a unique 3-dimensional shape that has squares for all six of its sides.

So, how do we find out how big a cube is? The answer to this question utilizes the object's volume. The volume of any cube can be determined as the amount of space the cube takes up or as the amount of space inside of the cube. Which definition applies to our examples? The volume of children's blocks or dice would both be described as the amount of space the cube takes up.

The milk crate pictured is an example of a cube whose volume could be described as the space inside of it. Cubic units are used when measuring volume. A milk crate has a volume of 1,728 cubic inches. This means that if you took a cube that had a side length of one inch, it would take 1,728 of them to fill up the milk crate. We will see later that calculating volume uses all three dimensions: length, width and height. This can also serve as a reminder to use cubic units, sometimes written as units^3.

Calculating Volume

To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times. This results in the formula: Volume = side * side * side. It is often written as V = s * s * s or V = s^3.

Let's see how this works with a real-life example. Imagine a teenager is told to put the socks scattered around a bedroom into a storage container. Will an empty milk crate provide enough space?

Let's calculate its volume. Each side of the crate has a measure of 12 inches. Substituting this value into the formula we get V = 12 * 12 * 12, or V = 12^3. This results in the volume of 1,728. Keep in mind we still need to use the appropriate units. Using cubic units would give us the volume of 1,728 cubic inches. This can also be written as 1,728 inches^3. A teenager could store 1,728 cubic inches of socks in the crate. I hope this makes mom happy!

Using the Formula

Let's try the formula with a few examples.

Example One

What is the volume of a cube with a side length of 4 centimeters?

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