115 LearnersLast updated on May 30th, 2025
Cube of 111
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 the cube of 111.
Cube of 111
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 111 can be written as 111³, which is the exponential form.
Or it can also be written in arithmetic form as, 111 × 111 × 111.
How to Calculate the Value of the Cube of 111
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 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 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. 111³ = 111 × 111 × 111
Step 2: Calculate the product. You get 1,367,631 as the answer. Hence, the cube of 111 is 1,367,631.
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 111 into two parts. Let a = 110 and b = 1, so a + b = 111
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 110³ 3a²b = 3 × 110² × 1 3ab² = 3 × 110 × 1² b³ = 1³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (110 + 1)³ = 110³ + 3 × 110² × 1 + 3 × 110 × 1² + 1³ 111³ = 1,331,000 + 36,300 + 330 + 1 111³ = 1,367,631
Step 5: Hence, the cube of 111 is 1,367,631.
Using a Calculator
To find the cube of 111 using a calculator, input the number 111 and use the cube function (if available) or multiply 111 × 111 × 111. This operation calculates the value of 111³, resulting in 1,367,631. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input the number 111.
Step 3: If the calculator has a cube function, press it to calculate 111³.
Step 4: If there is no cube function on the calculator, simply multiply 111 three times manually.
Step 5: The calculator will display 1,367,631.
Tips and Tricks for the Cube of 111
- 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 111
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, 111 × 111 and not 111 × 111 × 111. Always remember that 111³ = 111 × 111 × 111.
Solved Examples on Cube of 111
Problem 1
What is the cube and cube root of 111?
The cube of 111 is 1,367,631, and the cube root of 111 is approximately 4.805.
Explanation
First, let’s find the cube of 111.
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 111³ = 1,367,631. Next, we must find the cube root of 111.
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 ∛111 ≈ 4.805.
Hence, the cube of 111 is 1,367,631, and the cube root of 111 is approximately 4.805.
Problem 2
If the side length of a cube is 111 cm, what is the volume?
The volume is 1,367,631 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 111 for the side length: V = 111³ = 1,367,631 cm³.
Problem 3
How much larger is 111³ than 101³?
111³ – 101³ = 337,851.
Explanation
First, find the cube of 111³, which is 1,367,631.
Next, find the cube of 101³, which is 1,029,780.
Now, find the difference between them using the subtraction method. 1,367,631 – 1,029,780 = 337,851.
Therefore, 111³ is 337,851 larger than 101³.
Problem 4
If a cube with a side length of 111 cm is compared to a cube with a side length of 11 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 111 cm is 1,367,631 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 111 means multiplying 111 by itself three times: 111 × 111 = 12,321, and then 12,321 × 111 = 1,367,631.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,367,631 cm³.
Problem 5
Estimate the cube of 110.1 using the cube of 111.
The cube of 110.1 is approximately 1,367,631.
Explanation
First, identify the cube of 111.
The cube of 111 is 111³ = 1,367,631. Since 110.1 is only a tiny bit less than 111, the cube of 110.1 will be almost the same as the cube of 111.
The cube of 110.1 is approximately 1,367,631 because the difference between 110.1 and 111 is very small.
So, we can approximate the value as 1,367,631.
FAQs on Cube of 111
1.What are the perfect cubes up to 111?
2.How do you calculate 111³?
3.What is the meaning of 111³?
4.What is the cube root of 111?
5.Is 111 a perfect cube?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube of 111?
8.How do technology and digital tools in Thailand support learning Algebra and Cube of 111?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube of 111
- 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 cube of an integer.
- Cube Root: The number that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27.
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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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