101 LearnersLast updated on June 18th, 2025
Cube of 1001
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 1001.
Cube of 1001
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 1001 can be written as 1001³, which is the exponential form. Or it can also be written in arithmetic form as, 1001 × 1001 × 1001.
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
How to Calculate the Value of Cube of 1001
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.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of numbers 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. 1001³ = 1001 × 1001 × 1001
Step 2: You get 1,003,003,001 as the answer. Hence, the cube of 1001 is 1,003,003,001.
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 1001 into two parts. Let a = 1000 and b = 1, so a + b = 1001
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 1000³
3a²b = 3 × 1000² × 1
3ab² = 3 × 1000 × 1²
b³ = 1³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(1000 + 1)³ = 1000³ + 3 × 1000² × 1 + 3 × 1000 × 1² + 1³
1001³ = 1,000,000,000 + 3,000,000 + 3,000 + 1
1001³ = 1,003,003,001
Step 5: Hence, the cube of 1001 is 1,003,003,001.
Using a Calculator
To find the cube of 1001 using a calculator, input the number 1001 and use the cube function (if available) or multiply 1001 × 1001 × 1001. This operation calculates the value of 1001³, resulting in 1,003,003,001. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1, 0, 0, and 1
Step 3: If the calculator has a cube function, press it to calculate 1001³.
Step 4: If there is no cube function on the calculator, simply multiply 1001 three times manually.
Step 5: The calculator will display 1,003,003,001.
Tips and Tricks for the Cube of 1001
- 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.
Common Mistakes to Avoid When Calculating the Cube of 1001
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
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 1001 × 1001 and not 1001 × 1001 × 1001. Always remember that 1001³ = 1001 × 1001 × 1001.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility that kids might be confused between the formulas of square numbers and cube numbers. The square number formula is (a + b)² and the cube number formula is (a + b)³. Always review the formula for the difference between squaring and cubing.
Mistake 3
Calculator Misuse
Kids might press the wrong buttons, such as using the square (x²) function instead of the cube (x³) function or skipping steps in manual multiplication. Always double-check your inputs on the calculator, and if it lacks a cube function, perform the multiplication in steps.
Mistake 4
Misplacing Zeros
Misplacing zeros during manual multiplication can lead to incorrect results like 100,300,300 or 1,003,030,010 instead of 1,003,003,001. For this, kids should always double-check their answers.
Mistake 5
Ignoring the Binomial Formula
Kids might attempt to split 1001 into 1000 + 1, but not apply the correct binomial expansion. In order to avoid this, carefully calculate each term step-by-step during the application of the formula.
Level Up with a Math Certification!
2X Faster Learning (Grades 1-12)
Solved Examples on Cube of 1001
Problem 1
What is the cube and cube root of 1001?
The cube of 1001 is 1,003,003,001 and the cube root of 1001 is approximately 10.003.
Explanation
First, let’s find the cube of 1001.
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 1001³ = 1,003,003,001
Next, we must find the cube root of 1001.
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 ∛1001 ≈ 10.003
Hence the cube of 1001 is 1,003,003,001 and the cube root of 1001 is approximately 10.003.
Problem 2
If the side length of the cube is 1001 cm, what is the volume?
The volume is 1,003,003,001 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 1001 for the side length: V = 1001³ = 1,003,003,001 cm³.
Problem 3
How much larger is 1001³ than 999³?
1001³ – 999³ = 6,003,003.
Explanation
First, find the cube of 1001, which is 1,003,003,001.
Next, find the cube of 999, which is 997,002,999.
Now, find the difference between them using the subtraction method. 1,003,003,001 – 997,002,999 = 6,003,003
Therefore, 1001³ is 6,003,003 larger than 999³.
Problem 4
If a cube with a side length of 1001 cm is compared to a cube with a side length of 1 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1001 cm is 1,003,003,001 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1001 means multiplying 1001 by itself three times: 1001 × 1001 = 1,002,001, and then 1,002,001 × 1001 = 1,003,003,001.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,003,003,001 cm³.
Problem 5
Estimate the cube 1000.1 using the cube 1001.
The cube of 1000.1 is approximately 1,003,003,001.
Explanation
First, identify the cube of 1001, The cube of 1001 is 1001³ = 1,003,003,001.
Since 1000.1 is only a tiny bit less than 1001, the cube of 1000.1 will be almost the same as the cube of 1001.
The cube of 1000.1 is approximately 1,003,003,001 because the difference between 1000.1 and 1001 is very small.
So, we can approximate the value as 1,003,003,001.
Turn your child into a math star!
#1 Math Hack Schools Won't Teach!
FAQs on Cube of 1001
1.What are some perfect cubes up to 1001?
2.How do you calculate 1001³?
3.What is the meaning of 1001³?
4.What is the cube root of 1001?
5.Is 1001 a perfect cube?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 1001?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 1001?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
Important Glossaries for Cube of 1001
- Binomial Formula: An algebraic expression used to expand 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.
- Cube Root: An operation to determine a number that, when cubed, results in a given number. For example, the cube root of 8 is 2.
- Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice, such as 1, 8, 27, etc.
About BrightChamps in Saudi Arabia
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.
