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Last updated on June 3rd, 2025

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Cube of 221

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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 the cube of 221.

Cube of 221 for Bahraini Students
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Cube of 221

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 221 can be written as 221³, which is the exponential form. Or it can also be written in arithmetic form as, 221 × 221 × 221.

cube of 221

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How to Calculate the Value of Cube of 221

In order to check whether a number is a cube number or not, we can use the following three methods, such as the 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
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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.

221³ = 221 × 221 × 221

 

Step 2: You get 10,795,061 as the answer.

Hence, the cube of 221 is 10,795,061.

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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 221 into two parts, as 200 and 21. Let a = 200 and b = 21, so a + b = 221

 

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

 

Step 3: Calculate each term a³ = 200³ , 3a²b = 3 × 200² × 21 , 3ab² = 3 × 200 × 21² , b³ = 21³

 

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³

(200 + 21)³ = 200³ + 3 × 200² × 21 + 3 × 200 × 21² + 21³ 221³

= 8,000,000 + 2,520,000 + 264,600 + 9,261 221³ = 10,795,061

 

Step 5: Hence, the cube of 221 is 10,795,061.

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Using a Calculator

To find the cube of 221 using a calculator, input the number 221 and use the cube function (if available) or multiply 221 × 221 × 221. This operation calculates the value of 221³, resulting in 10,795,061. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 2, then 2, then 1

 

Step 3: If the calculator has a cube function, press it to calculate 221³.

 

Step 4: If there is no cube function on the calculator, simply multiply 221 three times manually.

 

Step 5: The calculator will display 10,795,061.

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Tips and Tricks for the Cube of 221

  • 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 221

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, 221 × 221 and not 221 × 221 × 221. Always remember that 221³ = 221 × 221 × 221.

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Solved Examples on Cube of 221

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Problem 1

What is the cube and cube root of 221?

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The cube of 221 is 10,795,061, and the cube root of 221 is approximately 6.004.

Explanation

First, let’s find the cube of 221.

We know that the cube of a number is such that x³ = y

Where x is the given number, and y is the cubed value of that number

So, we get 221³ = 10,795,061

Next, we must find the cube root of 221

We know that the cube root of a number ‘x’ is such that ∛x = y

Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ∛221 ≈ 6.004

Hence, the cube of 221 is 10,795,061, and the cube root of 221 is approximately 6.004.

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Problem 2

If the side length of the cube is 221 cm, what is the volume?

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The volume is 10,795,061 cm³.

Explanation

Use the volume formula for a cube V = side³.

Substitute 221 for the side length: V = 221³ = 10,795,061 cm³.

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Problem 3

How much larger is 221³ than 210³?

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221³ – 210³ = 1,891,971.

Explanation

First find the cube of 221, that is 10,795,061

Next, find the cube of 210, which is 9,103,090

Now, find the difference between them using the subtraction method.

10,795,061 – 9,103,090 = 1,891,971

Therefore, 221³ is 1,891,971 larger than 210³.

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Problem 4

If a cube with a side length of 221 cm is compared to a cube with a side length of 21 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 221 cm is 10,795,061 cm³.

Explanation

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

Cubing 221 means multiplying 221 by itself three times: 221 × 221 = 48,841, and then 48,841 × 221 = 10,795,061.

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

Therefore, the volume of the larger cube is 10,795,061 cm³.

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Problem 5

Estimate the cube of 220 using the cube of 221.

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The cube of 220 is approximately 10,648,000.

Explanation

First, identify the cube of 221, the cube of 221 is 221³ = 10,795,061.

Since 220 is very close to 221, the cube of 220 will be slightly less than the cube of 221.

The cube of 220 is approximately 10,648,000 because the difference between 220 and 221 is very small.

So, we can estimate the value as close to 10,648,000.

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FAQs on Cube of 221

1.What are the perfect cubes up to 221?

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2.How do you calculate 221³?

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3.What is the meaning of 221³?

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4.What is the cube root of 221?

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5.Is 221 a perfect cube?

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

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7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube of 221?

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8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 221?

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

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Important Glossaries for Cube of 221

  • Binomial Formula: It is 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: It is 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, which equals 8.

     
  • Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because it can be written as 3³.

     
  • Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
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About BrightChamps in Bahrain

At BrightChamps, algebra is more than just digits—it unlocks endless opportunities! We strive to help kids all across Bahrain develop key math skills, focusing today on the Cube of 221 with an exciting look at cubes—in a lively, clear, and enjoyable way. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, tracking football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence in everyday challenges. Our interactive lessons make math easy and fun. Because kids in Bahrain learn differently, we tailor our teaching to each child’s learning style. From Manama’s lively city life to Bahrain’s peaceful beaches, BrightChamps makes algebra come alive, making it exciting and relevant across Bahrain. Let’s make cubes a fun part of every child’s math journey!
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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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