### 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:

- 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:

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:

Hence, we have the formula:

V = L^{3}

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

### Math Video

#### Lesson Video

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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

#### Site-Search and Q&A Library

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