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103 LearnersLast updated on August 5, 2025
Cube of 1402
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 1402.
Cube of 1402
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 1402 can be written as 1402³, which is the exponential form. Or it can also be written in arithmetic form as, 1402 × 1402 × 1402.
How to Calculate the Value of Cube of 1402
In order to check whether a number is a cube number or not, we can use the following three methods, such as the 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 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. 1402³ = 1402 × 1402 × 1402
Step 2: Calculate the result. Hence, the cube of 1402 is 2,758,474,408.
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 1402 into two parts. Let a = 1400 and b = 2, so a + b = 1402
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 1400³ 3a²b = 3 × 1400² × 2 3ab² = 3 × 1400 × 2² b³ = 2³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (1400 + 2)³ = 1400³ + 3 × 1400² × 2 + 3 × 1400 × 2² + 2³ 1402³ = 2,744,000,000 + 11,760,000 + 16,800 + 8 1402³ = 2,758,474,408
Step 5: Hence, the cube of 1402 is 2,758,474,408.
Using a Calculator
To find the cube of 1402 using a calculator, input the number 1402 and use the cube function (if available) or multiply 1402 × 1402 × 1402. This operation calculates the value of 1402³, resulting in 2,758,474,408. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 1402.
Step 3: If the calculator has a cube function, press it to calculate 1402³.
Step 4: If there is no cube function on the calculator, simply multiply 1402 three times manually.
Step 5: The calculator will display 2,758,474,408.
Tips and Tricks for the Cube of 1402
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 1402
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, 1402 × 1402 and not 1402 × 1402 × 1402. Always remember that 1402³ = 1402 × 1402 × 1402.
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 leads to incorrect results. For this, kids should always double-check their answers.
Mistake 5
Ignoring the Binomial Formula
Kids might attempt to split the 1402 into 1400 + 2, 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.
Solved Examples on Cube of 1402
Problem 1
What is the cube and cube root of 1402?
The cube of 1402 is 2,758,474,408 and the cube root of 1402 is approximately 11.176.
Explanation
First, let’s find the cube of 1402. 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 1402³ = 2,758,474,408 Next, we must find the cube root of 1402.
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 ∛1402 ≈ 11.176 Hence the cube of 1402 is 2,758,474,408 and the cube root of 1402 is approximately 11.176.
Problem 2
If the side length of the cube is 1402 cm, what is the volume?
The volume is 2,758,474,408 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 1402 for the side length: V = 1402³ = 2,758,474,408 cm³.
Problem 3
How much larger is 1402³ than 1202³?
1402³ – 1202³ = 1,280,096,408.
Explanation
First, find the cube of 1402, that is 2,758,474,408. Next, find the cube of 1202, which is 1,478,378,000.
Now, find the difference between them using the subtraction method. 2,758,474,408 – 1,478,378,000 = 1,280,096,408.
Therefore, 1402³ is 1,280,096,408 larger than 1202³.
Problem 4
If a cube with a side length of 1402 cm is compared to a cube with a side length of 202 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1402 cm is 2,758,474,408 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 1402 means multiplying 1402 by itself three times: 1402 × 1402 = 1,965,604, and then 1,965,604 × 1402 = 2,758,474,408.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,758,474,408 cm³.
Problem 5
Estimate the cube of 1401.5 using the cube of 1402.
The cube of 1401.5 is approximately 2,758,474,408.
Explanation
First, identify the cube of 1402, The cube of 1402 is 1402³ = 2,758,474,408. Since 1401.5 is only a tiny bit less than 1402, the cube of 1401.5 will be almost the same as the cube of 1402.
The cube of 1401.5 is approximately 2,758,474,408 because the difference between 1401.5 and 1402 is very small. So, we can approximate the value as 2,758,474,408.
FAQs on Cube of 1402
1.What are the perfect cubes up to 1402?
2.How do you calculate 1402³?
3.What is the meaning of 1402³?
4.What is the cube root of 1402?
5.Is 1402 a perfect cube?
Important Glossaries for Cube of 1402
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Binomial Formula: Expands powers of expressions like (a + b)ⁿ, used to find squares and cubes.
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Cube of a Number: A number multiplied by itself three times.
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Exponential Form: Represents repeated multiplication using a base and exponent (e.g., 2³ = 2 × 2 × 2 = 8).
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Volume: Space occupied by a 3D object; for a cube, it is side³.
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Perfect Cube: A number that is the cube of an integer.
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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.
