114 LearnersLast updated on May 30th, 2025
Cube of 402
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 402.
Cube of 402
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 402 can be written as 4023, which is the exponential form.
Or it can also be written in arithmetic form as, 402 × 402 × 402.
How to Calculate the Value of Cube of 402
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 more easily without feeling confused or stuck while evaluating the answers.
- By Multiplication Method
- Using a Formula (a3)
- 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. 4023 = 402 × 402 × 402
Step 2: You get 65,029,608 as the answer. Hence, the cube of 402 is 65,029,608.
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 402 into two parts, such as (400) and (2). Let (a = 400) and (b = 2), so (a + b = 402)
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3)
Step 3: Calculate each term (a3 = 4003) (3a2b = 3 × 4002 × 2) (3ab2 = 3 × 400 × 22) (b3 = 23)
Step 4: Add all the terms together: (a + b)3 = a3 + 3a2b + 3ab2 + b3) (400 + 2)3 = 4003 + 3 × 4002 × 2 + 3 × 400 × 22 + 23) (4023 = 64,000,000 + 960,000 + 4,800 + 8) (4023 = 65,029,608)
Step 5: Hence, the cube of 402 is 65,029,608.
Using a Calculator
To find the cube of 402 using a calculator, input the number 402 and use the cube function (if available) or multiply 402 × 402 × 402. This operation calculates the value of 4023, resulting in 65,029,608. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 4 followed by 0 and 2.
Step 3: If the calculator has a cube function, press it to calculate 4023.
Step 4: If there is no cube function on the calculator, simply multiply 402 three times manually.
Step 5: The calculator will display 65,029,608.
Tips and Tricks for the Cube of 402
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 402
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, such as 402 × 402 instead of 402 × 402 × 402. Always remember that 4023 = 402 × 402 × 402.
Solved Examples on Cube of 402
Problem 1
What is the cube and cube root of 402?
The cube of 402 is 65,029,608 and the cube root of 402 is approximately 7.418.
Explanation
First, let’s find the cube of 402.
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 4023= 65,029,608.
Next, we must find the cube root of 402.
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 ∛402 ≈ 7.418.
Hence the cube of 402 is 65,029,608 and the cube root of 402 is approximately 7.418.
Problem 2
If the side length of the cube is 402 cm, what is the volume?
The volume is 65,029,608 cm³.
Explanation
Use the volume formula for a cube V = Side3.
Substitute 402 for the side length: V = 4023 = 65,029,608cm³.
Problem 3
How much larger is \(402^3\) than \(302^3\)?
4023 - 3023 = 47,161,608.
Explanation
First, find the cube of 4023, which is 65,029,608.
Next, find the cube of 3023, which is 17,868,000.
Now, find the difference between them using the subtraction method. 65,029,608 - 17,868,000 = 47,161,608.
Therefore, 4023 is 47,161,608 larger than 3023.
Problem 4
If a cube with a side length of 402 cm is compared to a cube with a side length of 102 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 402 cm is 65,029,608 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 402 means multiplying 402 by itself three times: 402 × 402 × 402 = 65,029,608.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 65,029,608 cm³.
Problem 5
Estimate the cube of 401.9 using the cube of 402.
The cube of 401.9 is approximately 65,029,608.
Explanation
First, identify the cube of 402.
The cube of 402 is 4023 = 65,029,608.
Since 401.9 is only a tiny bit less than 402, the cube of 401.9 will be almost the same as the cube of 402.
The cube of 401.9 is approximately 65,029,608 because the difference between 401.9 and 402 is very small.
So, we can approximate the value as 65,029,608.
FAQs on Cube of 402
1.What are the perfect cubes up to 402?
2.How do you calculate \(402^3\)?
3.What is the meaning of \(402^3\)?
4.What is the cube root of 402?
5.Is 402 a perfect cube?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube of 402?
8.How do technology and digital tools in Philippines support learning Algebra and Cube of 402?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube of 402
- Binomial Formula: 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: 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.
- Perfect Cube: A number that can be expressed as the product of three identical integers, such as 8 = 23.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of its side length.
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Jaskaran Singh Saluja
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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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