Volume of a Cube

Lesson Objective

In this lesson, we will learn about the volume of a cube.

About This Lesson

This lesson will explain the following things:

How to derive the formula for the volume of a cube
Using the formula to calculate the cube's volume
Using the volume formula to calculate the length of each side (edge) of a cube

The study tips and math video below will explain more.

Study Tips

Tip #1

In the last lesson, we learned that the volume (V) of a rectangular solid can be calculated by multiplying the width (W), length (L) and height (H) of the solid together. The formula is shown below:

V = WLH

rectangular solid with width W, length L and height H

Now, a cube is a special form of a rectangular solid because the sides (edges) of the cube have the same length. Therefore, if the length of a side of the cube is L, the width, length and height will have the length L.

With this, we can derive the formula for the volume of a cube as shown below:

V = WLH
= L×L×L
= L³

Hence, we have the formula:

V = L³

The math video below will explain more about this formula. Also, you will see some examples on using it...

Math Video

Lesson Video

If the above player doesn't work, try this direct link.

Math Video Transcript

00:00:04.170
In this lesson, we will learn how to find the volume of a cube.

00:00:09.000
First, consider this square with each side, with the length, L.

00:00:14.210
Now, we should already know that the area, A of this square is LxL.

00:00:21.110
Next, let's change this square into a cube.

00:00:25.190
Note that, all the sides of a cube have the same length, L.

00:00:30.220
To find the volume of the cube, we just need to multiply the area, A with L.

00:00:37.200
Hence, by multiplying these three 'L's together, we get L cube.

00:00:43.010
Therefore, the formula for the volume is, V = L cube.

00:00:52.190
Now, it is important that we include the unit for volume.

00:00:56.210
Since the unit for L is not given, we can write the unit for this volume as cubic unit.

00:01:03.040
Alright, let's take a look at some examples on how to find the volume of a cube.

00:01:08.220
Find the volume of this cube when the length of each side is 5cm. 

00:01:14.060
To solve this, we need to use the formula, V = L cube.

00:01:19.120
Now, since we know the length of each side of this cube is 5cm, we can substitute L with 5.

00:01:28.230
Next, 5 to the power of 3 is equals to, 5 multiply by 5 multiply by 5. This gives 125. Let's write it here.

00:01:41.090
Now, we have the volume as 125. Note that, this number is meaningless, unless we include the unit for it.

00:01:51.030
Since the unit for the length is in centimeter, the unit for the volume will be cubic centimeter.

00:01:57.070
Hence, the volume is 125 cubic cm. 

00:02:04.010
Next example, if the volume of the cube is 8 cubic ft, find the length of each side.

00:02:10.180
Now, let's start with the formula, V equals to L cube, where 'L' is the length of each side.

00:02:18.150
Since the volume of the cube is 8, we can substitute V with 8.

00:02:23.210
So, now we have, 8 = L cube.

00:02:28.000
To find 'L', we can see that since 8 is equals to 'L' cube,  L can be found by calculating the cube root of 8.

00:02:38.040
Before we continue, let's rewrite this equation properly by swapping these terms.

00:02:45.080
Next, cube root of 8 is 2.  So we have, L equals to 2.

00:02:52.120
Now, this number is meaningless, unless we include the unit for it.

00:02:57.210
Since the volume is in cubic feet, the length of the sides will be in feet.

00:03:03.000
Hence, the length of the sides is L = 2 ft. 

00:03:08.130
That is all for this lesson. Try out the practice question to test your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the volume of a cube or pick your choice of question below.

Question 1 on finding the volume of a cube
Question 2 on finding the length of the sides of a cube

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