116 LearnersLast updated on May 30th, 2025
Cube of 400
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 400.
Cube of 400
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 400 can be written as 400³, which is the exponential form.
Or it can also be written in arithmetic form as 400 × 400 × 400.
How to Calculate the Value of Cube of 400
In order to check whether a number is a cube number or not, we can use the following three methods, such as 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 (a3)
- 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. 400³ = 400 × 400 × 400
Step 2: You get 64,000,000 as the answer. Hence, the cube of 400 is 64,000,000.
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 400 into two parts. Let a = 300 and b = 100, so a + b = 400
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 300³ 3a²b = 3 × 300² × 100 3ab² = 3 × 300 × 100² b³ = 100³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (300 + 100)³ = 300³ + 3 × 300² × 100 + 3 × 300 × 100² + 100³ 400³ = 27,000,000 + 27,000,000 + 9,000,000 + 1,000,000 400³ = 64,000,000
Step 5: Hence, the cube of 400 is 64,000,000.
Using a Calculator
To find the cube of 400 using a calculator, input the number 400 and use the cube function (if available) or multiply 400 × 400 × 400. This operation calculates the value of 400³, resulting in 64,000,000. 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, 0
Step 3: If the calculator has a cube function, press it to calculate 400³.
Step 4: If there is no cube function on the calculator, simply multiply 400 three times manually.
Step 5: The calculator will display 64,000,000.
Tips and Tricks for the Cube of 400
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 400
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, 400 × 400 and not 400 × 400 × 400. Always remember that 400³ = 400 × 400 × 400.
Solved Examples on Cube of 400
Problem 1
What is the cube and cube root of 400?
The cube of 400 is 64,000,000 and the cube root of 400 is approximately 7.368.
Explanation
First, let’s find the cube of 400.
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 400³ = 64,000,000 Next, we must find the cube root of 400
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 ∛400 ≈ 7.368
Hence the cube of 400 is 64,000,000 and the cube root of 400 is approximately 7.368.
Problem 2
If the side length of the cube is 400 cm, what is the volume?
The volume is 64,000,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 400 for the side length: V = 400³ = 64,000,000 cm³.
Problem 3
How much larger is 400³ than 300³?
400³ – 300³ = 37,000,000.
Explanation
First find the cube of 400³, that is 64,000,000
Next, find the cube of 300³, which is 27,000,000
Now, find the difference between them using the subtraction method. 64,000,000 – 27,000,000 = 37,000,000
Therefore, the 400³ is 37,000,000 larger than 300³.
Problem 4
If a cube with a side length of 400 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 400 cm is 64,000,000 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 400 means multiplying 400 by itself three times: 400 × 400 = 160,000, and then 160,000 × 400 = 64,000,000.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 64,000,000 cm³.
Problem 5
Estimate the cube of 399.9 using the cube of 400.
The cube of 399.9 is approximately 64,000,000.
Explanation
First, identify the cube of 400, The cube of 400 is 400³ = 64,000,000.
Since 399.9 is only a tiny bit less than 400, the cube of 399.9 will be almost the same as the cube of 400.
The cube of 399.9 is approximately 64,000,000 because the difference between 399.9 and 400 is very small.
So, we can approximate the value as 64,000,000.
FAQs on Cube of 400
1.What are the perfect cubes up to 400?
2.How do you calculate 400³?
3.What is the meaning of 400³?
4.What is the cube root of 400?
5.Is 400 a perfect cube?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube of 400?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube of 400?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube of 400
- 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.
- Cube Root: A value that, when multiplied by itself three times, gives the original number. For example, the cube root of 64 is 4, because 4 × 4 × 4 equals 64.
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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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