101 LearnersLast updated on June 3rd, 2025
Cube of 118
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 118.
Cube of 118
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 118 can be written as 118³, which is the exponential form.
Or it can also be written in arithmetic form as, 118 × 118 × 118.
How to Calculate the Value of Cube of 118
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. 118³ = 118 × 118 × 118
Step 2: You get 1,646,072 as the answer. Hence, the cube of 118 is 1,646,072.
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 118 into two parts, as and . Let a = 110 and b = 8, so a + b = 118
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 110³ 3a²b = 3 × 110² × 8 3ab² = 3 × 110 × 8² b³ = 8³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (110 + 8)³ = 110³ + 3 × 110² × 8 + 3 × 110 × 8² + 8³ 118³ = 1,331,000 + 290,400 + 21,120 + 512 118³ = 1,646,072
Step 5: Hence, the cube of 118 is 1,646,072.
Using a Calculator
To find the cube of 118 using a calculator, input the number 118 and use the cube function (if available) or multiply 118 × 118 × 118. This operation calculates the value of 118³, resulting in 1,646,072. 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 8
Step 3: If the calculator has a cube function, press it to calculate 118³.
Step 4: If there is no cube function on the calculator, simply multiply 118 three times manually.
Step 5: The calculator will display 1,646,072.
Tips and Tricks for the Cube of 118
- 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 118
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, 118 × 118 and not 118 × 118 × 118. Always remember that 118³ = 118 × 118 × 118.
Solved Examples on Cube of 118
Problem 1
What is the cube and cube root of 118?
The cube of 118 is 1,646,072 and the cube root of 118 is approximately 4.857.
Explanation
First, let’s find the cube of 118. 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 118³ = 1,646,072
Next, we must find the cube root of 118
We know that the cube root of a number ‘x’, such that ³√x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ³√118 ≈ 4.857
Hence the cube of 118 is 1,646,072 and the cube root of 118 is approximately 4.857.
Problem 2
If the side length of the cube is 118 cm, what is the volume?
The volume is 1,646,072 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 118 for the side length: V = 118³ = 1,646,072 cm³.
Problem 3
How much larger is 118³ than 108³?
118³ – 108³ = 542,944.
Explanation
First, find the cube of 118³, that is 1,646,072
Next, find the cube of 108³, which is 1,103,128
Now, find the difference between them using the subtraction method. 1,646,072 – 1,103,128 = 542,944
Therefore, 118³ is 542,944 larger than 108³.
Problem 4
If a cube with a side length of 118 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 118 cm is 1,646,072 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 118 means multiplying 118 by itself three times: 118 × 118 = 13,924, and then 13,924 × 118 = 1,646,072.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,646,072 cm³.
Problem 5
Estimate the cube of 117 using the cube of 118.
The cube of 117 is approximately 1,646,072.
Explanation
First, identify the cube of 118,
The cube of 118 is 118³ = 1,646,072.
Since 117 is only a tiny bit less than 118, the cube of 117 will be almost the same as the cube of 118.
The cube of 117 is approximately 1,646,072 because the difference between 117 and 118 is very small.
So, we can approximate the value as 1,646,072.
FAQs on Cube of 118
1.What are the perfect cubes up to 118?
2.How do you calculate 118³?
3.What is the meaning of 118³?
4.What is the cube root of 118?
5.Is 118 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 118?
8.How do technology and digital tools in United States support learning Algebra and Cube of 118?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 118
- 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, which equals 8.
- Perfect Cube: A number that can be expressed as the product of three equal integers.
- Volume of a Cube: The amount of space inside a cube, calculated as the side length cubed.
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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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