100 LearnersLast updated on June 3rd, 2025
Cube of 219
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 219.
Cube of 219
A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times. When you cube a positive number, the result is always positive. When you cube a negative number, the result is always negative. This is because a negative number multiplied by itself three times results in a negative number. The cube of 219 can be written as 219³, which is the exponential form. Or it can also be written in arithmetic form as 219 × 219 × 219.
How to Calculate the Value of Cube of 219
In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number.
219³ = 219 × 219 × 219
Step 2: You get 10,503,459 as the answer.
Hence, the cube of 219 is 10,503,459.
Using a Formula (a³)
The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.
Step 1: Split the number 219 into two parts, as 200 and 19. Let a = 200 and b = 19, so a + b = 219
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ , 3a²b = 3 × 200² × 19 , 3ab² = 3 × 200 × 19² , b³ = 19³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(200 + 19)³= 200³ + 3 × 200² × 19 + 3 × 200 × 19² + 19³ 219³
= 8,000,000 + 2,280,000 + 216,600 + 6,859 219³ = 10,503,459
Step 5: Hence, the cube of 219 is 10,503,459.
Using a Calculator
To find the cube of 219 using a calculator, input the number 219 and use the cube function (if available) or multiply 219 × 219 × 219. This operation calculates the value of 219³, resulting in 10,503,459. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2 followed by 1 and 9
Step 3: If the calculator has a cube function, press it to calculate 219³.
Step 4: If there is no cube function on the calculator, simply multiply 219 three times manually.
Step 5: The calculator will display 10,503,459.
Tips and Tricks for the Cube of 219
The cube of any even number is always even, while the cube of any odd number is always odd. The product of two or more perfect cube numbers is always a perfect cube. A perfect cube can always be expressed as the product of three identical groups of equal prime factors.
Common Mistakes to Avoid When Calculating the Cube of 219
There are some typical errors that kids might make during the process of cubing a number. Let us take a look at five of the major mistakes that kids might make:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 219 × 219 and not 219 × 219 × 219. Always remember that 219³ = 219 × 219 × 219.
Solved Examples on Cube of 219
Problem 1
What is the cube and cube root of 219?
The cube of 219 is 10,503,459 and the cube root of 219 is approximately 6.000.
Explanation
First, let’s find the cube of 219.
We know that the cube of a number, such that x³ = y
Where x is the given number, and y is the cubed value of that number
So, we get 219³ = 10,503,459
Next, we must find the cube root of 219
We know that the cube root of a number ‘x’, such that ³√x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ³√219 ≈ 6.000
Hence the cube of 219 is 10,503,459 and the cube root of 219 is approximately 6.000.
Problem 2
If the side length of the cube is 219 cm, what is the volume?
The volume is 10,503,459 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 219 for the side length: V = 219³ = 10,503,459 cm³.
Problem 3
How much larger is 219³ than 120³?
219³ - 120³ = 10,503,459 - 1,728,000 = 8,775,459.
Explanation
First, find the cube of 219³, that is 10,503,459.
Next, find the cube of 120³, which is 1,728,000.
Now, find the difference between them using the subtraction method.
10,503,459 - 1,728,000 = 8,775,459
Therefore, 219³ is 8,775,459 larger than 120³.
Problem 4
If a cube with a side length of 219 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 219 cm is 10,503,459 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 219 means multiplying 219 by itself three times: 219 × 219 = 47,961, and then 47,961 × 219 = 10,503,459.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 10,503,459 cm³.
Problem 5
Estimate the cube of 218.9 using the cube of 219.
The cube of 218.9 is approximately 10,503,459.
Explanation
First, identify the cube of 219, The cube of 219 is 219³ = 10,503,459.
Since 218.9 is only a tiny bit less than 219, the cube of 218.9 will be almost the same as the cube of 219.
The cube of 218.9 is approximately 10,503,459 because the difference between 218.9 and 219 is very small.
So, we can approximate the value as 10,503,459.
FAQs on Cube of 219
1.What are the perfect cubes up to 219?
2.How do you calculate 219³?
3.What is the meaning of 219³?
4.What is the cube root of 219?
5.Is 219 a perfect cube?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 219?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 219?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 219
- Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
- Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
- Exponential Form: A way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of its side length.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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