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Last updated on May 26th, 2025

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Cube of 502

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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 in comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 502.

Cube of 502 for UAE Students
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Cube of 502

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 502 can be written as 502^3, which is the exponential form. Or it can also be written in arithmetic form as 502 × 502 × 502.

 

cube of 502

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How to Calculate the Value of Cube of 502

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.

 

  1. By Multiplication Method
  2. Using a Formula
  3. 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. 5023 = 502 × 502 × 502

 

Step 2: You get 126,503,008 as the answer. Hence, the cube of 502 is 126,503,008.

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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 502 into two parts, such as 500 and 2. Let a = 500 and b = 2, so a + b = 502

 

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

 

Step 3: Calculate each term

 

a3 = 5003

 

3a2b = 3 × 5002 × 2

 

3ab2 = 3 × 500 × 22

 

b3 = 23

 

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

 

(500 + 2)3 = 5003 + 3 × 5002 × 2 + 3 × 500 × 22 + 23

 

5023 = 125,000,000 + 1,500,000 + 6,000 + 8

 

5023 = 126,503,008

 

Step 5: Hence, the cube of 502 is 126,503,008.

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Using a Calculator

To find the cube of 502 using a calculator, input the number 502 and use the cube function (if available) or multiply 502 × 502 × 502. This operation calculates the value of 5023, resulting in 126,503,008. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 5 followed by 0 and 2

 

Step 3: If the calculator has a cube function, press it to calculate 5023.

 

Step 4: If there is no cube function on the calculator, simply multiply 502 three times manually.

 

Step 5: The calculator will display 126,503,008.

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Tips and Tricks for the Cube of 502

  • 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 502

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, 502 × 502 and not 502 × 502 × 502. Always remember that 5023 = 502 × 502 × 502.

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Solved Examples on Cube of 502

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Problem 1

What is the cube and cube root of 502?

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The cube of 502 is 126,503,008 and the cube root of 502 is approximately 7.937.

Explanation

First, let’s find the cube of 502. 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 5023 = 126,503,008

 

Next, we must find the cube root of 502. 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 ∛502 ≈ 7.937

 

Hence the cube of 502 is 126,503,008 and the cube root of 502 is approximately 7.937.

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Problem 2

If the side length of the cube is 502 cm, what is the volume?

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The volume is 126,503,008 cm³.

Explanation

Use the volume formula for a cube V = side3.

 

Substitute 502 for the side length: V = 5023 = 126,503,008 cm³.

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Problem 3

How much larger is 502^3 than 402^3?

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5023 – 4023 = 61,008,008.

Explanation

First find the cube of 502, which is 126,503,008. Next, find the cube of 402, which is 65,495,000. Now, find the difference between them using the subtraction method. 126,503,008 – 65,495,000 = 61,008,008.

 

Therefore, 5023 is 61,008,008 larger than 4023.

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Problem 4

If a cube with a side length of 502 cm is compared to a cube with a side length of 10 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 502 cm is 126,503,008 cm³.

Explanation

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

 

Cubing 502 means multiplying 502 by itself three times: 502 × 502 = 252,004, and then 252,004 × 502 = 126,503,008. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.

 

Therefore, the volume of the cube is 126,503,008 cm³.

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Problem 5

Estimate the cube of 501.9 using the cube of 502.

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The cube of 501.9 is approximately 126,503,008.

Explanation

First, identify the cube of 502.

 

The cube of 502 is 502^3 = 126,503,008.

 

Since 501.9 is only a tiny bit less than 502, the cube of 501.9 will be almost the same as the cube of 502. The cube of 501.9 is approximately 126,503,008 because the difference between 501.9 and 502 is very small.

 

So, we can approximate the value as 126,503,008.

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FAQs on Cube of 502

1.What are the perfect cubes up to 502?

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2.How do you calculate 502^3?

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3.What is the meaning of 502^3?

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4.What is the cube root of 502?

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5.Is 502 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 502?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube of 502?

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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 502

  • 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 equals 8.

 

  • Perfect Cube: A number that can be expressed as the cube of an integer.

 

  • Volume: The amount of space inside a three-dimensional object, measured in cubic units. For a cube, it is calculated as side3.
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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 502, 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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