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Last updated on May 30th, 2025

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Cube of 224

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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 cubes of 224.

Cube of 224 for Vietnamese Students
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Cube of 224

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 by itself three times results in a negative number.

 

The cube of 224 can be written as 224³, which is the exponential form.

 

Or it can also be written in arithmetic form as, 224 × 224 × 224.

cube of 224

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How to Calculate the Value of Cube of 224

In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These 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 (a3)
     
  • Using a Calculator
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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. 224³ = 224 × 224 × 224

 

Step 2: You get 11,238,784 as the answer.

 

Hence, the cube of 224 is 11,238,784.

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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 224 into two parts, as 200 and 24. Let a = 200 and b = 24, so a + b = 224

 

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

 

Step 3: Calculate each term a³ = 200³ 3a²b = 3 × 200² × 24 3ab² = 3 × 200 × 24² b³ = 24³

 

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (200 + 24)³ = 200³ + 3 × 200² × 24 + 3 × 200 × 24² + 24³ 224³ = 8,000,000 + 2,880,000 + 345,600 + 13,824 224³ = 11,238,784

 

Step 5: Hence, the cube of 224 is 11,238,784.

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Using a Calculator

To find the cube of 224 using a calculator, input the number 224 and use the cube function (if available) or multiply 224 × 224 × 224. This operation calculates the value of 224³, resulting in 11,238,784. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 2, 2, and 4

 

Step 3: If the calculator has a cube function, press it to calculate 224³.

 

Step 4: If there is no cube function on the calculator, simply multiply 224 three times manually.

 

Step 5: The calculator will display 11,238,784.

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Tips and Tricks for the Cube of 224

  • 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.
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Common Mistakes to Avoid When Calculating the Cube of 224

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

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Incorrect Multiplication

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Kids might multiply the numbers only twice. That is, 224 × 224 and not 224 × 224 × 224. Always remember that 224³ = 224 × 224 × 224.

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Solved Examples on Cube of 224

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Problem 1

What is the cube and cube root of 224?

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The cube of 224 is 11,238,784, and the cube root of 224 is approximately 6.000.

Explanation

First, let’s find the cube of 224.

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 224³ = 11,238,784.

Next, we must find the cube root of 224.

We know that the cube root of a number x, such that ∛x = y,

where x is the given number, and y is the cube root value of the number.

So, we get ∛224 ≈ 6.000.

Hence, the cube of 224 is 11,238,784, and the cube root of 224 is approximately 6.000.

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Problem 2

If the side length of the cube is 224 cm, what is the volume?

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The volume is 11,238,784 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 224 for the side length: V = 224³ = 11,238,784 cm³.

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Problem 3

How much larger is 224³ than 200³?

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224³ – 200³ = 3,238,784.

Explanation

First, find the cube of 224³, which is 11,238,784.

Next, find the cube of 200³, which is 8,000,000.

Now, find the difference between them using the subtraction method. 11,238,784 – 8,000,000 = 3,238,784.

Therefore, 224³ is 3,238,784 larger than 200³.

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Problem 4

If a cube with a side length of 224 cm is compared to a cube with a side length of 24 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 224 cm is 11,238,784 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 224 means multiplying 224 by itself three times: 224 × 224 = 50,176, and 50,176 × 224 = 11,238,784.

The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.

Therefore, the volume of the cube is 11,238,784 cm³.

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Problem 5

Estimate the cube of 223.9 using the cube of 224.

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The cube of 223.9 is approximately 11,238,784.

Explanation

First, identify the cube of 224.

The cube of 224 is 224³ = 11,238,784.

Since 223.9 is only a tiny bit less than 224, the cube of 223.9 will be almost the same as the cube of 224.

The cube of 223.9 is approximately 11,238,784 because the difference between 223.9 and 224 is very small.

So, we can approximate the value as 11,238,784.

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FAQs on Cube of 224

1.What are the perfect cubes up to 224?

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2.How do you calculate 224³?

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3.What is the meaning of 224³?

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4.What is the cube root of 224?

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5.Is 224 a perfect cube?

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6.How does learning Algebra help students in Vietnam make better decisions in daily life?

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7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of 224?

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8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 224?

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9.Does learning Algebra support future career opportunities for students in Vietnam?

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Professor Greenline from BrightChamps

Important Glossaries for Cube of 224

  • 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. For example, 8 is a perfect cube because it is 2³.

 

  • Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3 because 3³ = 27.
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About BrightChamps in Vietnam

At BrightChamps, we believe algebra is more than just numbers—it’s a way to unlock countless chances! We aim to assist children across Vietnam in understanding key math concepts, like today’s focus on the Cube of 224, with a special emphasis on cubes—in a fun, clear, and engaging way. Whether your child is calculating the speed of a roller coaster at Suoi Tien Theme Park, following the scores at a local football match, or managing their allowance to buy the latest gadgets, learning algebra builds their confidence for everyday challenges. Our interactive lessons make math easy and fun. Because kids in Vietnam learn differently, we personalize our teaching to match each child’s style. From Ho Chi Minh City’s lively streets to the beautiful landscapes of Ha Long Bay, BrightChamps brings algebra to life, making it exciting and relevant throughout Vietnam. Let’s make cubes a fun part of every child’s math adventure!
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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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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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