Volume of a Cube
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.
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 = L3
The math video below will explain more about this formula. Also, you will see some examples on using it...
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Math Video Transcript
In this lesson, we will learn how to find the volume of a cube.
First, consider this square with each side, with the length, L.
Now, we should already know that the area, A of this square is LxL.
Next, let's change this square into a cube.
Note that, all the sides of a cube have the same length, L.
To find the volume of the cube, we just need to multiply the area, A with L.
Hence, by multiplying these three 'L's together, we get L cube.
Therefore, the formula for the volume is, V = L cube.
Now, it is important that we include the unit for volume.
Since the unit for L is not given, we can write the unit for this volume as cubic unit.
Alright, let's take a look at some examples on how to find the volume of a cube.
Find the volume of this cube when the length of each side is 5cm.
To solve this, we need to use the formula, V = L cube.
Now, since we know the length of each side of this cube is 5cm, we can substitute L with 5.
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.
Now, we have the volume as 125. Note that, this number is meaningless, unless we include the unit for it.
Since the unit for the length is in centimeter, the unit for the volume will be cubic centimeter.
Hence, the volume is 125 cubic cm.
Next example, if the volume of the cube is 8 cubic ft, find the length of each side.
Now, let's start with the formula, V equals to L cube, where 'L' is the length of each side.
Since the volume of the cube is 8, we can substitute V with 8.
So, now we have, 8 = L cube.
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.
Before we continue, let's rewrite this equation properly by swapping these terms.
Next, cube root of 8 is 2. So we have, L equals to 2.
Now, this number is meaningless, unless we include the unit for it.
Since the volume is in cubic feet, the length of the sides will be in feet.
Hence, the length of the sides is L = 2 ft.
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.
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