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103 LearnersLast updated on August 5, 2025
Cube of 1403
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 1403.
Cube of 1403
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 1403 can be written as 1403³, which is the exponential form. Or it can also be written in arithmetic form as, 1403 × 1403 × 1403.
How to Calculate the Value of Cube of 1403
To calculate 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 you to cube 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. 1403³ = 1403 × 1403 × 1403
Step 2: Calculate the result. You will get 2,763,364,227 as the answer. Hence, the cube of 1403 is 2,763,364,227.
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 1403 into two parts, as, for example, 1400 and 3. Let a = 1400 and b = 3, so a + b = 1403
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 1400³ 3a²b = 3 × 1400² × 3 3ab² = 3 × 1400 × 3² b³ = 3³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (1400 + 3)³ = 1400³ + 3 × 1400² × 3 + 3 × 1400 × 3² + 3³ 1403³ = 2,744,000,000 + 17,640,000 + 37,800 + 27 1403³ = 2,763,364,227
Step 5: Hence, the cube of 1403 is 2,763,364,227.
Using a Calculator
To find the cube of 1403 using a calculator, input the number 1403 and use the cube function (if available) or multiply 1403 × 1403 × 1403. This operation calculates the value of 1403³, resulting in 2,763,364,227. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 1, 4, 0, 3
Step 3: If the calculator has a cube function, press it to calculate 1403³.
Step 4: If there is no cube function on the calculator, simply multiply 1403 three times manually.
Step 5: The calculator will display 2,763,364,227.
Tips and Tricks for the Cube of 1403
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 1403
There are some typical errors that might occur during the process of cubing a number. Let's take a look at five major mistakes to avoid:
Mistake 1
Incorrect Multiplication
You might multiply the numbers only twice, that is, 1403 × 1403 and not 1403 × 1403 × 1403. Always remember that 1403³ = 1403 × 1403 × 1403.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility of confusion 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
You 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 2,763,364,27 instead of 2,763,364,227. Always double-check your answers.
Mistake 5
Ignoring the Binomial Formula
You might attempt to split 1403 into 1400 + 3 but not apply the correct binomial expansion. Carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 1403
Problem 1
What is the cube and cube root of 1403?
The cube of 1403 is 2,763,364,227 and the cube root of 1403 is approximately 11.145.
Explanation
First, let’s find the cube of 1403. 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 1403³ = 2,763,364,227.
Next, we must find the cube root of 1403. 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√1403 ≈ 11.145.
Hence, the cube of 1403 is 2,763,364,227 and the cube root of 1403 is approximately 11.145.
Problem 2
If the side length of the cube is 1403 cm, what is the volume?
The volume is 2,763,364,227 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 1403 for the side length: V = 1403³ = 2,763,364,227 cm³.
Problem 3
How much larger is 1403³ than 1000³?
1403³ – 1000³ = 2,763,364,227 - 1,000,000,000 = 1,763,364,227.
Explanation
First, find the cube of 1403, which is 2,763,364,227. Next, find the cube of 1000, which is 1,000,000,000.
Now, find the difference between them using the subtraction method. 2,763,364,227 - 1,000,000,000 = 1,763,364,227.
Therefore, 1403³ is 1,763,364,227 larger than 1000³.
Problem 4
If a cube with a side length of 1403 cm is compared to a cube with a side length of 3 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1403 cm is 2,763,364,227 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 1403 means multiplying 1403 by itself three times: 1403 × 1403 = 1,969,609, and then 1,969,609 × 1403 = 2,763,364,227.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 2,763,364,227 cm³.
Problem 5
Estimate the cube of 1402 using the cube of 1403.
The cube of 1402 is approximately 2,763,364,227.
Explanation
First, identify the cube of 1403. The cube of 1403 is 1403³ = 2,763,364,227. Since 1402 is only slightly less than 1403, the cube of 1402 will be almost the same as the cube of 1403.
The cube of 1402 is approximately 2,763,364,227 because the difference between 1402 and 1403 is very small. So, we can approximate the value as 2,763,364,227.
FAQs on Cube of 1403
1.What are the perfect cubes up to 1403?
2.How do you calculate 1403³?
3.What is the meaning of 1403³?
4.What is the cube root of 1403?
5.Is 1403 a perfect cube?
Important Glossaries for Cube of 1403
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Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer.
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Cube of a Number: Multiplying a number by itself three times.
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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.
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Perfect Cube: A number that can be expressed as the cube of an integer.
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Volume: The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great.
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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.
