100 LearnersLast updated on May 26th, 2025
Cube of 501
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 cubes of 501.
Cube of 501
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 501 can be written as 501³, which is the exponential form. Or it can also be written in arithmetic form as, 501 × 501 × 501.
How to Calculate the Value of Cube of 501
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 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. 501³ = 501 × 501 × 501
Step 2: You get 125,751,501 as the answer. Hence, the cube of 501 is 125,751,501.
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 501 into two parts. Let a = 500 and b = 1, so a + b = 501
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ 3a²b = 3 × 500² × 1 3ab² = 3 × 500 × 1² b³ = 1³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(500 + 1)³ = 500³ + 3 × 500² × 1 + 3 × 500 × 1² + 1³
501³ = 125,000,000 + 750,000 + 1,500 + 1
501³ = 125,751,501
Step 5: Hence, the cube of 501 is 125,751,501.
Using a Calculator
To find the cube of 501 using a calculator, input the number 501 and use the cube function (if available) or multiply 501 × 501 × 501. This operation calculates the value of 501³, resulting in 125,751,501. 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 0 and 1
Step 3: If the calculator has a cube function, press it to calculate 501³.
Step 4: If there is no cube function on the calculator, simply multiply 501 three times manually.
Step 5: The calculator will display 125,751,501.
Tips and Tricks for the Cube of 501
- 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 501
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, 501 × 501 and not 501 × 501 × 501. Always remember that 501³ = 501 × 501 × 501.
Solved Examples on Cube of 501
Problem 1
What is the cube and cube root of 501?
The cube of 501 is 125,751,501 and the cube root of 501 is approximately 7.937.
Explanation
First, let’s find the cube of 501.
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 501³ = 125,751,501.
Next, we must find the cube root of 501.
We know that the cube root of a number ‘x’, such that ³√x = y, where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ³√501 ≈ 7.937. Hence the cube of 501 is 125,751,501 and the cube root of 501 is approximately 7.937.
Problem 2
If the side length of the cube is 501 cm, what is the volume?
The volume is 125,751,501 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 501 for the side length: V = 501³ = 125,751,501 cm³.
Problem 3
How much larger is 501³ than 400³?
501³ – 400³ = 93,351,501.
Explanation
First find the cube of 501, which is 125,751,501. Next, find the cube of 400, which is 64,000,000.
Now, find the difference between them using the subtraction method.
125,751,501 – 64,000,000 = 61,751,501.
Therefore, 501³ is 61,751,501 larger than 400³.
Problem 4
If a cube with a side length of 501 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 501 cm is 125,751,501 cm³, which is significantly larger.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 501 means multiplying 501 by itself three times: 501 × 501 = 251,001, and then 251,001 × 501 = 125,751,501.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 125,751,501 cm³.
Problem 5
Estimate the cube of 500.9 using the cube of 501.
The cube of 500.9 is approximately 125,751,501.
Explanation
First, identify the cube of 501, The cube of 501 is 501³ = 125,751,501.
Since 500.9 is only a tiny bit less than 501, the cube of 500.9 will be almost the same as the cube of 501.
The cube of 500.9 is approximately 125,751,501 because the difference between 500.9 and 501 is very small.
So, we can approximate the value as 125,751,501.
FAQs on Cube of 501
1.What are the perfect cubes up to 501?
2.How do you calculate 501³?
3.What is the meaning of 501³?
4.What is the cube root of 501?
5.Is 501 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 501?
8.How do technology and digital tools in Philippines support learning Algebra and Cube of 501?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube of 501
- 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.
- Volume of a Cube: The amount of space inside a cube, calculated as the side length raised to the power of three (Side³).
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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.
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