Cube of 1003
2026-02-28 01:25 Diff
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Last updated on August 5, 2025

When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 1003.

Cube of 1003

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 1003 can be written as 1003³, which is the exponential form. Or it can also be written in arithmetic form as, 1003 × 1003 × 1003.

How to Calculate the Value of Cube of 1003

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.

  1. By Multiplication Method
  2. Using a Formula
  3. 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. 1003³ = 1003 × 1003 × 1003

Step 2: You get 1,009,027,027 as the answer. Hence, the cube of 1003 is 1,009,027,027.

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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 1003 into two parts. Let a = 1000 and b = 3, so a + b = 1003

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

Step 3: Calculate each term

a³ = 1000³

3a²b = 3 × 1000² × 3

3ab² = 3 × 1000 × 3²

b³ = 3³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(1000 + 3)³ = 1000³ + 3 × 1000² × 3 + 3 × 1000 × 3² + 3³

1003³ = 1,000,000,000 + 9,000,000 + 27,000 + 27

1003³ = 1,009,027,027

Step 5: Hence, the cube of 1003 is 1,009,027,027.

Using a Calculator

To find the cube of 1003 using a calculator, input the number 1003 and use the cube function (if available) or multiply 1003 × 1003 × 1003. This operation calculates the value of 1003³, resulting in 1,009,027,027. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1 followed by 0, 0, and 3

Step 3: If the calculator has a cube function, press it to calculate 1003³.

Step 4: If there is no cube function on the calculator, simply multiply 1003 three times manually.

Step 5: The calculator will display 1,009,027,027.

Tips and Tricks for the Cube of 1003

  • 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 1003

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:

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Problem 1

What is the cube and cube root of 1003?

Okay, lets begin

The cube of 1003 is 1,009,027,027 and the cube root of 1003 is approximately 10.003.

Explanation

First, let’s find the cube of 1003.

We know that 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 1003³ = 1,009,027,027

Next, we must find the cube root of 1003

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√1003 ≈ 10.003

Hence the cube of 1003 is 1,009,027,027 and the cube root of 1003 is approximately 10.003.

Well explained 👍

Problem 2

If the side length of the cube is 1003 cm, what is the volume?

Okay, lets begin

The volume is 1,009,027,027 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 1003 for the side length: V = 1003³ = 1,009,027,027 cm³.

Well explained 👍

Problem 3

How much larger is 1003³ than 1000³?

Okay, lets begin

1003³ – 1000³ = 27,027.

Explanation

First, find the cube of 1003, which is 1,009,027,027

Next, find the cube of 1000, which is 1,000,000,000

Now, find the difference between them using the subtraction method. 1,009,027,027 – 1,000,000,000 = 27,027

Therefore, the 1003³ is 27,027 larger than 1000³.

Well explained 👍

Problem 4

If a cube with a side length of 1003 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 1003 cm is 1,009,027,027 cm³.

Explanation

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

Cubing 1003 means multiplying 1003 by itself three times: 1003 × 1003 = 1,006,009, and then 1,006,009 × 1003 = 1,009,027,027.

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

Therefore, the volume of the cube is 1,009,027,027 cm³.

Well explained 👍

Problem 5

Estimate the cube 1002.9 using the cube 1003.

Okay, lets begin

The cube of 1002.9 is approximately 1,009,027,027.

Explanation

First, identify the cube of 1003, The cube of 1003 is 1003³ = 1,009,027,027.

Since 1002.9 is only a tiny bit less than 1003, the cube of 1002.9 will be almost the same as the cube of 1003.

The cube of 1002.9 is approximately 1,009,027,027 because the difference between 1002.9 and 1003 is very small.

So, we can approximate the value as 1,009,027,027.

Well explained 👍

FAQs on Cube of 1003

1.What are the perfect cubes up to 1000?

The perfect cubes up to 1000 are 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 1003³?

To calculate 1003³, use the multiplication method, 1003 × 1003 × 1003, which equals 1,009,027,027.

3.What is the meaning of 1003³?

1003³ means 1003 multiplied by itself three times, or 1003 × 1003 × 1003.

4.What is the cube root of 1003?

The cube root of 1003 is approximately 10.003.

5.Is 1003 a perfect cube?

No, 1003 is not a perfect cube because no integer multiplied by itself three times equals 1003.

Important Glossaries for Cube of 1003

  • 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. For example, 27 is a perfect cube since it is 3³.
  • Cube Root: A number that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.

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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.

Fun Fact

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