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Last updated on June 3rd, 2025

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Cube of 114

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When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 114.

Cube of 114 for US Students
Professor Greenline from BrightChamps

Cube of 114

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 114 can be written as 114³, which is the exponential form.

 

Or it can also be written in arithmetic form as, 114 × 114 × 114.

cube of 114

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How to Calculate the Value of Cube of 114

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 to cube the numbers faster and more easily without confusion or getting stuck while evaluating the answers.

 

  • By Multiplication Method
     
  • Using a Formula
     
  • Using a Calculator
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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. 114³ = 114 × 114 × 114

 

Step 2: Calculate the product. You get 1,480,584 as the answer.

 

Hence, the cube of 114 is 1,480,584.

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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 114 into two parts. Let a = 110 and b = 4, so a + b = 114

 

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

 

Step 3: Calculate each term a³ = 110³ 3a²b = 3 × 110² × 4 3ab² = 3 × 110 × 4² b³ = 4³

 

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (110 + 4)³ = 110³ + 3 × 110² × 4 + 3 × 110 × 4² + 4³ 114³ = 1,331,000 + 145,200 + 5,280 + 64 114³ = 1,480,544

 

Step 5: Hence, the cube of 114 is 1,480,544.

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Using a Calculator

To find the cube of 114 using a calculator, input the number 114 and use the cube function (if available) or multiply 114 × 114 × 114. This operation calculates the value of 114³, resulting in 1,480,544. 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 4

 

Step 3: If the calculator has a cube function, press it to calculate 114³.

 

Step 4: If there is no cube function on the calculator, simply multiply 114 three times manually.

 

Step 5: The calculator will display 1,480,544.

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Tips and Tricks for the Cube of 114

  • 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.
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Common Mistakes to Avoid When Calculating the Cube of 114

There are some typical errors that might occur during the process of cubing a number. Let us take a look at some major mistakes:

Mistake 1

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Incorrect Multiplication

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There might be a mistake in multiplying the numbers only twice, such as 114 × 114 and not 114 × 114 × 114. Always remember that 114³ = 114 × 114 × 114.

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Solved Examples on Cube of 114

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Problem 1

What is the cube and cube root of 114?

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The cube of 114 is 1,480,544 and the cube root of 114 is approximately 4.879.

Explanation

First, let’s find the cube of 114.

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 114³ = 1,480,544 Next, we must find the cube root of 114

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 ∛114 ≈ 4.879

Hence, the cube of 114 is 1,480,544 and the cube root of 114 is approximately 4.879.

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Problem 2

If the side length of the cube is 114 cm, what is the volume?

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The volume is 1,480,544 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 114 for the side length: V = 114³ = 1,480,544 cm³.

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Problem 3

How much larger is 114³ than 100³?

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114³ – 100³ = 480,544.

Explanation

First, find the cube of 114³, which is 1,480,544

Next, find the cube of 100³, which is 1,000,000

Now, find the difference between them using the subtraction method. 1,480,544 – 1,000,000 = 480,544

Therefore, 114³ is 480,544 larger than 100³.

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Problem 4

If a cube with a side length of 114 cm is compared to a cube with a side length of 50 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 114 cm is larger by 1,355,544 cm³.

Explanation

To find the volume of the larger cube, multiply the side length by itself three times.

Cubing 114 means multiplying 114 by itself three times: 114 × 114 = 12,996, and then 12,996 × 114 = 1,480,544.

The volume of the smaller cube (side length 50 cm) is 125,000 cm³.

Therefore, the larger cube's volume is 1,480,544 cm³ – 125,000 cm³ = 1,355,544 cm³ larger.

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Problem 5

Estimate the cube of 113.5 using the cube of 114.

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The cube of 113.5 is approximately 1,480,000.

Explanation

First, identify the cube of 114,

The cube of 114 is 114³ = 1,480,544.

Since 113.5 is only slightly less than 114, the cube of 113.5 will be almost the same as the cube of 114.

The cube of 113.5 is approximately 1,480,000 due to the small difference between 113.5 and 114.

So, we can approximate the value as 1,480,000.

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FAQs on Cube of 114

1.What are the perfect cubes up to 114?

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2.How do you calculate 114³?

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3.What is the meaning of 114³?

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4.What is the cube root of 114?

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5.Is 114 a perfect cube?

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6.How does learning Algebra help students in United States make better decisions in daily life?

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7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 114?

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8.How do technology and digital tools in United States support learning Algebra and Cube of 114?

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9.Does learning Algebra support future career opportunities for students in United States?

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Professor Greenline from BrightChamps

Important Glossaries for Cube of 114

  • 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 used as a factor three times, results in the original number.
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About BrightChamps in United States

At BrightChamps, we believe algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to support kids all across the United States in mastering essential math concepts, like today’s focus on the Cube of 114, especially the fascinating world of cubes—in a way that’s engaging, clear, and enjoyable. Whether your child is calculating how quickly a roller coaster zooms through Disney World, tracking scores at a Little League baseball game, or budgeting their allowance for new gadgets, understanding algebra builds the confidence they need for daily life. Our hands-on lessons make math both accessible and fun. Since children in the USA learn in diverse ways, we customize our teaching to match each student’s learning style. From the energetic streets of New York City to the sunny beaches of California, BrightChamps brings algebra to life, making it exciting and relevant across America. Let’s make cubes an exciting part of every child’s math journey!
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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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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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