117 LearnersLast updated on May 28th, 2025
Cube of 481
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 481.
Cube of 481
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 481 can be written as 481³, which is the exponential form. Or it can also be written in arithmetic form as, 481 × 481 × 481.
How to Calculate the Value of Cube of 481
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 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. 481³ = 481 × 481 × 481
Step 2: You get 111,980,561 as the answer. Hence, the cube of 481 is 111,980,561.
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 481 into two parts, as and . Let a = 480 and b = 1, so a + b = 481
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 480³
3a²b = 3 × 480² × 1
3ab² = 3 × 480 × 1²
b³ = 1³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(480 + 1)³ = 480³ + 3 × 480² × 1 + 3 × 480 × 1² + 1³
481³ = 110,592,000 + 691,200 + 1,440 + 1
481³ = 111,980,561
Step 5: Hence, the cube of 481 is 111,980,561.
Using a Calculator
To find the cube of 481 using a calculator, input the number 481 and use the cube function (if available) or multiply 481 × 481 × 481. This operation calculates the value of 481³, resulting in 111,980,561. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 4, then 8, then 1.
Step 3: If the calculator has a cube function, press it to calculate 481³.
Step 4: If there is no cube function on the calculator, simply multiply 481 three times manually.
Step 5: The calculator will display 111,980,561.
Tips and Tricks for the Cube of 481
- 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 481
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might happen:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice. That is, 481 × 481 and not 481 × 481 × 481. Always remember that 481³ = 481 × 481 × 481.
Solved Examples on Cube of 481
Problem 1
What is the cube and cube root of 481?
The cube of 481 is 111,980,561 and the cube root of 481 is approximately 7.82.
Explanation
First, let’s find the cube of 481.
We know that 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 481³ = 111,980,561 Next, we must find the cube root of 481 We know that 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 √481 ≈ 7.82
Hence the cube of 481 is 111,980,561 and the cube root of 481 is approximately 7.82.
Problem 2
If the side length of the cube is 481 cm, what is the volume?
The volume is 111,980,561 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 481 for the side length: V = 481³ = 111,980,561 cm³.
Problem 3
How much larger is 481³ than 380³?
481³ – 380³ = 60,839,161.
Explanation
First find the cube of 481³, which is 111,980,561
Next, find the cube of 380³, which is 51,141,400
Now, find the difference between them using the subtraction method.
111,980,561 – 51,141,400 = 60,839,161
Therefore, the 481³ is 60,839,161 larger than 380³.
Problem 4
If a cube with a side length of 481 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 481 cm is 111,980,561 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 481 means multiplying 481 by itself three times: 481 × 481 = 231,361, and then 231,361 × 481 = 111,980,561.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 111,980,561 cm³.
Problem 5
Estimate the cube of 480.9 using the cube of 481.
The cube of 480.9 is approximately 111,980,561.
Explanation
First, identify the cube of 481, The cube of 481 is 481³ = 111,980,561.
Since 480.9 is only a tiny bit less than 481, the cube of 480.9 will be almost the same as the cube of 481.
The cube of 480.9 is approximately 111,980,561 because the difference between 480.9 and 481 is very small.
So, we can approximate the value as 111,980,561.
FAQs on Cube of 481
1.What are the perfect cubes up to 481?
2.How do you calculate 481³?
3.What is the meaning of 481³?
4.What is the cube root of 481?
5.Is 481 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 481?
8.How do technology and digital tools in United States support learning Algebra and Cube of 481?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 481
- 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 product of three identical numbers.
- Volume: The amount of space occupied by a three-dimensional object, typically measured in cubic units.
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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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