100 LearnersLast updated on June 2nd, 2025
Cube of 510
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 cubes of 510.
Cube of 510
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 510 can be written as 510³, which is the exponential form. Or it can also be written in arithmetic form as, 510 × 510 × 510.
How to Calculate the Value of Cube of 510
In order 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 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 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.
510³ = 510 × 510 × 510
Step 2: You get 132,651,000 as the answer.
Hence, the cube of 510 is 132,651,000.
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 510 into two parts.
Let a = 500 and b = 10, so a + b = 510
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 10 , , 3ab² = 3 × 500 × 10² , b³ = 10³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(500 + 10)³ = 500³ + 3 × 500² × 10 + 3 × 500 × 10² + 10³ 510³
= 125,000,000 + 7,500,000 + 150,000 + 1,000 510³
= 132,651,000
Step 5: Hence, the cube of 510 is 132,651,000.
Using a Calculator
To find the cube of 510 using a calculator, input the number 510 and use the cube function (if available) or multiply 510 × 510 × 510. This operation calculates the value of 510³, resulting in 132,651,000. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 5 followed by 1 and 0
b If the calculator has a cube function, press it to calculate 510³.
Step 4: If there is no cube function on the calculator, simply multiply 510 three times manually.
Step 5: The calculator will display 132,651,000.
Tips and Tricks for the Cube of 510
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 510
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, 510 × 510 and not 510 × 510 × 510. Always remember that 510³ = 510 × 510 × 510.
Solved Examples on Cube of 510
Problem 1
What is the cube and cube root of 510?
The cube of 510 is 132,651,000 and the cube root of 510 is approximately 7.958.
Explanation
First, let’s find the cube of 510.
We know that the cube of a number is x³ = y
Where x is the given number, and y is the cubed value of that number
So, we get 510³ = 132,651,000
Next, we must find the cube root of 510
We know that the cube root of a number ‘x’ is ∛x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ∛510 ≈ 7.958
Hence, the cube of 510 is 132,651,000 and the cube root of 510 is approximately 7.958.
Problem 2
If the side length of the cube is 510 cm, what is the volume?
The volume is 132,651,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 510 for the side length: V = 510³ = 132,651,000 cm³.
Problem 3
How much larger is 510³ than 500³?
510³ – 500³ = 7,651,000.
Explanation
First find the cube of 510, which is 132,651,000
Next, find the cube of 500, which is 125,000,000
Now, find the difference between them using the subtraction method.
132,651,000 – 125,000,000 = 7,651,000
Therefore, 510³ is 7,651,000 larger than 500³.
Problem 4
If a cube with a side length of 510 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 510 cm is 132,651,000 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 510 means multiplying 510 by itself three times: 510 × 510 = 260,100, and 260,100 × 510 = 132,651,000.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 132,651,000 cm³.
Problem 5
Estimate the cube of 509.9 using the cube of 510.
The cube of 509.9 is approximately 132,651,000.
Explanation
First, identify the cube of 510, The cube of 510 is 510³ = 132,651,000.
Since 509.9 is only a tiny bit less than 510, the cube of 509.9 will be almost the same as the cube of 510.
The cube of 509.9 is approximately 132,651,000 because the difference between 509.9 and 510 is very small.
So, we can approximate the value as 132,651,000.
FAQs on Cube of 510
1.What are the perfect cubes up to 510?
2.How do you calculate 510³?
3.What is the meaning of 510³?
4.What is the cube root of 510?
5.Is 510 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 510?
8.How do technology and digital tools in United States support learning Algebra and Cube of 510?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 510
- 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. For example, 2³ represents 2 × 2 × 2 equals 8.
- Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice more. For example, 8 is a perfect cube because it is 2 × 2 × 2.
- Cube Root: A value that, when multiplied by itself twice, gives the original number. It is denoted as ∛.
Explore More algebra
Previous to Cube of 510
Next to Cube of 510
About BrightChamps in United States
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.
