102 LearnersLast updated on May 26th, 2025
Cube of 492
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 the cube of 492.
Cube of 492
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 492 can be written as 492³, which is the exponential form. Or it can also be written in arithmetic form as, 492 × 492 × 492.
How to Calculate the Value of Cube of 492
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
- 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. 492³ = 492 × 492 × 492
Step 2: You get 118,523,328 as the answer. Hence, the cube of 492 is 118,523,328.
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 492 into two parts, such as 490 and 2. Let a = 490 and b = 2, so a + b = 492
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 490³ 3a²b = 3 × 490² × 2 3ab² = 3 × 490 × 2² b³ = 2³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(490 + 2)³ = 490³ + 3 × 490² × 2 + 3 × 490 × 2² + 2³
492³ = 117,649,000 + 1,440,600 + 5,880 + 8
492³ = 118,523,328
Step 5: Hence, the cube of 492 is 118,523,328.
Using a Calculator
To find the cube of 492 using a calculator, input the number 492 and use the cube function (if available) or multiply 492 × 492 × 492. This operation calculates the value of 492³, resulting in 118,523,328. 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 9 and 2
Step 3: If the calculator has a cube function, press it to calculate 492³.
Step 4: If there is no cube function on the calculator, simply multiply 492 three times manually.
Step 5: The calculator will display 118,523,328.
Tips and Tricks for the Cube of 492
- 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 492
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, 492 × 492 and not 492 × 492 × 492. Always remember that 492³ = 492 × 492 × 492.
Solved Examples on Cube of 492
Problem 1
What is the cube and cube root of 492?
The cube of 492 is 118,523,328 and the cube root of 492 is approximately 7.88.
Explanation
First, let’s find the cube of 492.
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 492³ = 118,523,328.
Next, we must find the cube root of 492.
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 ∛492 ≈ 7.88. Hence, the cube of 492 is 118,523,328, and the cube root of 492 is approximately 7.88.
Problem 2
If the side length of the cube is 492 cm, what is the volume?
The volume is 118,523,328 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 492 for the side length: V = 492³ = 118,523,328 cm³.
Problem 3
How much larger is 492³ than 490³?
492³ – 490³ = 2,814,328.
Explanation
First, find the cube of 492, which is 118,523,328.
Next, find the cube of 490, which is 117,649,000.
Now, find the difference between them using the subtraction method.
118,523,328 – 117,649,000 = 874,328.
Therefore, 492³ is 874,328 larger than 490³.
Problem 4
If a cube with a side length of 492 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 492 cm is 118,523,328 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 492 means multiplying 492 by itself three times: 492 × 492 = 242,064, and 242,064 × 492 = 118,523,328.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 118,523,328 cm³.
Problem 5
Estimate the cube of 491.5 using the cube of 492.
The cube of 491.5 is approximately 118,523,328.
Explanation
First, identify the cube of 492, The cube of 492 is 492³ = 118,523,328.
Since 491.5 is only a tiny bit less than 492, the cube of 491.5 will be almost the same as the cube of 492.
The cube of 491.5 is approximately 118,523,328 because the difference between 491.5 and 492 is very small.
So, we can approximate the value as 118,523,328.
FAQs on Cube of 492
1.What are the perfect cubes up to 492?
2.How do you calculate 492³?
3.What is the meaning of 492³?
4.What is the cube root of 492?
5.Is 492 a perfect cube?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Cube of 492?
8.How do technology and digital tools in Qatar support learning Algebra and Cube of 492?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Cube of 492
- 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: The number that, when multiplied by itself three times, gives the original number.
Explore More algebra
Previous to Cube of 492
Next to Cube of 492
About BrightChamps in Qatar
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.
