Cubes from 1 to 20

The cube is an integer you get when multiplying the same integer three times by itself. Like, a³ =  a x a x a. The cubes of 1 to 20 come in between 13 = 1 and 203 = 8000. The cubes in exponential form are represented as x³. The smallest cube in topic is 1³ and the largest cube is 20³. 

In this topic, students do not have to remember the results of the cubes. The students must understand the concept of cubes and how to calculate the cubes to get the correct results. Let us now see the list of cubes from 1 to 20.

Cubes from 1 to 10

Studying cubes from 1 to 10 are important for volume calculations and understanding 3D shapes. Let’s explore the cube of numbers from 1 to 10.

Cubes from 11 to 20

The cube numbers from 11 to 20 are commonly used in calculations involving larger volumes and measurements.

Let’s see the cube of numbers from 11 to 20.

Even numbers are the numbers that can be divided by 2 without leaving any remainder. The even numbers from 1 to 20 are 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20. Learning the cubes of the even numbers that come in between 1 and 20 is also significant. Let us now see the table that shows the cubes of the even numbers that come in between 1 and 20.

Odd numbers are the numbers that leave a remainder while dividing said numbers by 2. The odd numbers from 1 to 20 are 3, 5, 7, 9, 11, 13, 15, 17 and 19. Students must know that learning the cubes of the odd numbers that come in between 1 and 20 is also significant. Let us now see the table that shows the cubes of the odd numbers that come in between 1 and 20.

The cubes of a certain number can be calculated by using two methods. The list of the methods are mentioned below:

• Multiplication Method

• Pattern Recognition Method
   

This multiplication method includes a cube of a number by itself 3 times to find its cube, use the below steps to determine a cube of a number.

Step 1: First write the number which we need to multiply. For example, 4

Step 2: Multiply the number 4 itself to get 42. Now, 4 x 4 = 16.
    
  

Step 3: Multiplying the result in step 2 with the number 4 to get the result. So, 16 x 4 = 64.

Therefore, 43 = 64

Pattern recognition is identifying repeating patterns in numbers. Using the below pattern recognition method, the cube of a number can be obtained:

Step 1: The formula to find the cube of a number by using a pattern method is 
(n² - n) + 1. Here, n is any number which we require to find a cube.

For example, to find the cube of 3
3³ = (3² - 3) + 1= (9 -3) +1 = 6 + 1 = 7

Step 2: The sequence of odd numbers begins at 7 and continues up to 3 numbers.
Now, 3³ = 7 + 9 + 11= 27

So, the cube of 3 is 27

To understand the concept of cubes, there are specific rules that have to be followed. Some of the rules the students must know are given below:

Understanding Exponents

Students might wrongly think cubes with squares. A square is a number multiplied by itself two times (a2), while a cube is a number multiplied by itself three times (a³).

Using the Cube Formula: (a³ = a x a x a)

Students should know the cube of a number is the product of the same number when it is multiplied by itself thrice. Such as, 43 = 4 x 4 x 4.

Identifying Patterns in Cubes
Cubes can be written as the sum of consecutive odd numbers. For example, 33 = 27 can be expressed as 7 + 9 + 11 = 27. In this case, the sequence of odd numbers starts from 7 and continues for 3 numbers to equal the cube of 3.

Sometimes students find it difficult to understand the concept of cubes. Here are some tips and tricks students can use to reduce the difficulty in understanding the concept of cubes.

Visualize a cube:

Think of a3 as the volume of a cube with the side length a. For example, 2³ = 2 x 2 x 2 = 8. Which means, a cube has 2 units and has a volume of 8 cubic units.

Memorize Small Cubes: 

Students can start by learning small cubes, as it helps them to gain confidence in finding the cubes of larger numbers.

Shortcut for Estimation:

If the students are finding trouble to find the cubes for larger numbers like 20. The students can use this shortcut to find the cube: 20³ = 20 x 20 = 40 and then multiply 40 with 20 to get the cube: 40 x 20 = 800.