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Last updated on May 30th, 2025

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Cube of 413

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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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 413.

Cube of 413 for UAE Students
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Cube of 413

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 413 can be written as 4133, which is the exponential form.

 

Or it can also be written in arithmetic form as, 413 × 413 × 413.

cube of 413

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How to Calculate the Value of Cube of 413

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 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 (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. 4133 = 413 × 413 × 413

 

Step 2: You get 70,381,997 as the answer. Hence, the cube of 413 is 70,381,997.

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Using a Formula (a^3)

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 413 into two parts, as 400 and 13. Let a = 400 and b = 13, so a + b = 413

 

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

 

Step 3: Calculate each term a^3 = 400^3 3a^2b = 3 × 400^2 × 13 3ab^2 = 3 × 400 × 13^2 b^3 = 13^3

 

Step 4: Add all the terms together: (a + b)^3 = a3 + 3a2b + 3ab2 + b3 (400 + 13)3 = 4003 + 3 × 4002 × 13 + 3 × 400 × 132 + 133 4133 = 64,000,000 + 6,240,000 + 202,800 + 2,197 4133 = 70,381,997

 

Step 5: Hence, the cube of 413 is 70,381,997.

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Using a Calculator

To find the cube of 413 using a calculator, input the number 413 and use the cube function (if available) or multiply 413 × 413 × 413. This operation calculates the value of 413^3, resulting in 70,381,997. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Input 413

 

Step 3: If the calculator has a cube function, press it to calculate 413^3.

 

Step 4: If there is no cube function on the calculator, simply multiply 413 three times manually.

 

Step 5: The calculator will display 70,381,997.

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Tips and Tricks for the Cube of 413

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 413

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, 413 × 413 and not 413 × 413 × 413. Always remember that 4133 = 413 × 413 × 413.

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Solved Examples on Cube of 413

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Problem 1

What is the cube and cube root of 413?

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The cube of 413 is 70,381,997 and the cube root of 413 is approximately 7.4485.

Explanation

First, let’s find the cube of 413.

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 4133 = 70,381,997.

Next, we must find the cube root of 413.

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 ∛413 ≈ 7.4485.

Hence, the cube of 413 is 70,381,997 and the cube root of 413 is approximately 7.4485.

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Problem 2

If the side length of the cube is 413 cm, what is the volume?

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The volume is 70,381,997 cm^3.

Explanation

Use the volume formula for a cube V = Side3.

Substitute 413 for the side length: V = 4133 = 70,381,997 cm3.

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Problem 3

How much larger is 413^3 than 400^3?

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4133 – 4003 = 6,381,997.

Explanation

First, find the cube of 4133, which is 70,381,997.

Next, find the cube of 4003, which is 64,000,000.

Now, find the difference between them using the subtraction method. 70,381,997 – 64,000,000 = 6,381,997.

Therefore, 4133 is 6,381,997 larger than 4003.

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Problem 4

If a cube with a side length of 413 cm is compared to a cube with a side length of 13 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 413 cm is 70,381,997 cm^3.

Explanation

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

Cubing 413 means multiplying 413 by itself three times: 413 × 413 = 170,569, and then 170,569 × 413 = 70,381,997.

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

Therefore, the volume of the cube is 70,381,997 cm3.

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Problem 5

Estimate the cube of 412.9 using the cube of 413.

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The cube of 412.9 is approximately 70,381,997.

Explanation

First, identify the cube of 413.

The cube of 413 is 4133 = 70,381,997.

Since 412.9 is only a tiny bit less than 413, the cube of 412.9 will be almost the same as the cube of 413.

The cube of 412.9 is approximately 70,381,997 because the difference between 412.9 and 413 is very small.

So, we can approximate the value as 70,381,997.

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FAQs on Cube of 413

1.What are the perfect cubes up to 413?

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2.How do you calculate 413^3?

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3.What is the meaning of 413^3?

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4.What is the cube root of 413?

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5.Is 413 a perfect cube?

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6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?

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7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Cube of 413?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube of 413?

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9.Does learning Algebra support future career opportunities for students in United Arab Emirates?

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Important Glossaries for Cube of 413

  • 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, 33 represents 3 × 3 × 3 equals 27.

 

  • Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted as ∛x.

 

  • Perfect Cube: A perfect cube is a number that can be expressed as the cube of an integer.
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About BrightChamps in United Arab Emirates

At BrightChamps, algebra is more than just digits—it’s a gateway to infinite possibilities! We focus on helping kids across the UAE develop essential math skills, with today’s spotlight on the Cube of 413, especially exploring cubes—in a lively, simple, and enjoyable manner. Whether your child is working out the speed of a roller coaster at Dubai Parks and Resorts, keeping track of scores at local sports events, or managing their allowance for the latest gadgets, mastering algebra helps them gain confidence in daily life. Our interactive lessons make math fun and accessible. Because children in the UAE learn differently, we adapt our teaching to fit their individual learning styles. From Dubai’s towering skyscrapers to Abu Dhabi’s cultural heritage, BrightChamps makes algebra come alive across the UAE. Let’s make cubes a delightful 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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