101 LearnersLast updated on June 3rd, 2025
Cube of 113
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 cubes of 113.
Cube of 113
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 113 can be written as 113³, which is the exponential form.
Or it can also be written in arithmetic form as, 113 × 113 × 113.
How to Calculate the Value of Cube of 113
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. 113³ = 113 × 113 × 113
Step 2: You get 1,446,087 as the answer. Hence, the cube of 113 is 1,446,087.
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 113 into two parts, as a and b. Let a = 100 and b = 13, so a + b = 113
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 13 3ab² = 3 × 100 × 13² b³ = 13³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 13)³ = 100³ + 3 × 100² × 13 + 3 × 100 × 13² + 13³ 113³ = 1,000,000 + 390,000 + 50,700 + 2,197 113³ = 1,446,897
Step 5: Hence, the cube of 113 is 1,446,897.
Using a Calculator
To find the cube of 113 using a calculator, input the number 113 and use the cube function (if available) or multiply 113 × 113 × 113. This operation calculates the value of 113³, resulting in 1,446,897. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1 followed by 1 and 3
Step 3: If the calculator has a cube function, press it to calculate 113³.
Step 4: If there is no cube function on the calculator, simply multiply 113 three times manually.
Step 5: The calculator will display 1,446,897.
Tips and Tricks for the Cube of 113
- 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 113
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, 113 × 113 and not 113 × 113 × 113. Always remember that 113³ = 113 × 113 × 113.
Solved Examples on Cube of 113
Problem 1
What is the cube and cube root of 113?
The cube of 113 is 1,446,897 and the cube root of 113 is approximately 4.82.
Explanation
First, let’s find the cube of 113.
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 113³ = 1,446,897
Next, we must find the cube root of 113
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 ∛113 ≈ 4.82
Hence the cube of 113 is 1,446,897, and the cube root of 113 is approximately 4.82.
Problem 2
If the side length of the cube is 113 cm, what is the volume?
The volume is 1,446,897 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 113 for the side length: V = 113³ = 1,446,897 cm³.
Problem 3
How much larger is 113³ than 100³?
113³ – 100³ = 446,897.
Explanation
First find the cube of 113, that is 1,446,897
Next, find the cube of 100, which is 1,000,000
Now, find the difference between them using the subtraction method. 1,446,897 – 1,000,000 = 446,897
Therefore, 113³ is 446,897 larger than 100³.
Problem 4
If a cube with a side length of 113 cm is compared to a cube with a side length of 50 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 113 cm is 1,446,897 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 113 means multiplying 113 by itself three times: 113 × 113 = 12,769, and then 12,769 × 113 = 1,446,897.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,446,897 cm³.
Problem 5
Estimate the cube of 112.9 using the cube of 113.
The cube of 112.9 is approximately 1,446,897.
Explanation
First, identify the cube of 113,
The cube of 113 is 113³ = 1,446,897.
Since 112.9 is only a tiny bit less than 113, the cube of 112.9 will be almost the same as the cube of 113.
The cube of 112.9 is approximately 1,446,897 because the difference between 112.9 and 113 is very small.
So, we can approximate the value as 1,446,897.
FAQs on Cube of 113
1.What are the perfect cubes up to 113?
2.How do you calculate 113³?
3.What is the meaning of 113³?
4.What is the cube root of 113?
5.Is 113 a perfect cube?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube of 113?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube of 113?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube of 113
- 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 to 8.
- Volume of a Cube: The amount of space enclosed within a cube, calculated as the cube of its side length.
- Perfect Cube: A number that is the cube of an integer.
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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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