114 LearnersLast updated on May 30th, 2025
Cube of 407
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 407.
Cube of 407
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 407 can be written as 407³, which is the exponential form.
Or it can also be written in arithmetic form as, 407 × 407 × 407.
How to Calculate the Value of Cube of 407
In order to check whether a number is a cube number or not, we can use the following three methods: 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 (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. 407³ = 407 × 407 × 407
Step 2: You get 67,209,743 as the answer. Hence, the cube of 407 is 67,209,743.
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 407 into two parts, as 400 and 7. Let a = 400 and b = 7, so a + b = 407
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 7 3ab² = 3 × 400 × 7² b³ = 7³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 7)³ = 400³ + 3 × 400² × 7 + 3 × 400 × 7² + 7³ 407³ = 64,000,000 + 33,600 + 5,880 + 343 407³ = 67,209,743
Step 5: Hence, the cube of 407 is 67,209,743.
Using a Calculator
To find the cube of 407 using a calculator, input the number 407 and use the cube function (if available) or multiply 407 × 407 × 407. This operation calculates the value of 407³, resulting in 67,209,743. 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 7
Step 3: If the calculator has a cube function, press it to calculate 407³.
Step 4: If there is no cube function on the calculator, simply multiply 407 three times manually.
Step 5: The calculator will display 67,209,743.
Tips and Tricks for the Cube of 407
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 407
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, 407 × 407 and not 407 × 407 × 407. Always remember that 407³ = 407 × 407 × 407.
Solved Examples on Cube of 407
Problem 1
What is the cube and cube root of 407?
The cube of 407 is 67,209,743 and the cube root of 407 is approximately 7.406.
Explanation
First, let’s find the cube of 407.
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 407³ = 67,209,743 Next, we must find the cube root of 407.
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 ∛407 ≈ 7.406
Hence the cube of 407 is 67,209,743, and the cube root of 407 is approximately 7.406.
Problem 2
If the side length of a cube is 407 cm, what is the volume?
The volume is 67,209,743 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 407 for the side length: V = 407³ = 67,209,743 cm³.
Problem 3
How much larger is 407³ than 400³?
407³ – 400³ = 209,743.
Explanation
First, find the cube of 407, which is 67,209,743.
Next, find the cube of 400, which is 64,000,000.
Now, find the difference between them using the subtraction method. 67,209,743 – 64,000,000 = 209,743
Therefore, 407³ is 209,743 larger than 400³.
Problem 4
If a cube with a side length of 407 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 407 cm is 67,209,743 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 407 means multiplying 407 by itself three times: 407 × 407 = 165,649, and then 165,649 × 407 = 67,209,743.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 67,209,743 cm³.
Problem 5
Estimate the cube of 406.9 using the cube of 407.
The cube of 406.9 is approximately 67,209,743.
Explanation
First, identify the cube of 407, The cube of 407 is 407³ = 67,209,743.
Since 406.9 is only a tiny bit less than 407, the cube of 406.9 will be almost the same as the cube of 407.
The cube of 406.9 is approximately 67,209,743 because the difference between 406.9 and 407 is very small.
So, we can approximate the value as 67,209,743.
FAQs on Cube of 407
1.What are the perfect cubes up to 407?
2.How do you calculate 407³?
3.What is the meaning of 407³?
4.What is the cube root of 407?
5.Is 407 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 407?
8.How do technology and digital tools in United States support learning Algebra and Cube of 407?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 407
- 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: The result of 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: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
- Perfect Cube: A number that can be expressed as the cube of an integer is called a perfect cube.
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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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