117 LearnersLast updated on May 30th, 2025
Cube of 102
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 102.
Cube of 102
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 102 can be written as 102³, which is the exponential form.
Or it can also be written in arithmetic form as, 102 × 102 × 102.
How to Calculate the Value of Cube of 102
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 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 (a3)
- Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of numbers 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. 102³ = 102 × 102 × 102
Step 2: You get 1,061,208 as the answer.
Hence, the cube of 102 is 1,061,208.
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 102 into two parts. Let a = 100 and b = 2, so a + b = 102
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 2 3ab² = 3 × 100 × 2² b³ = 2³
Step 4: Add all the terms together: (100 + 2)³ = 100³ + 3 × 100² × 2 + 3 × 100 × 2² + 2³ 102³ = 1,000,000 + 60,000 + 1,200 + 8 102³ = 1,061,208
Step 5: Hence, the cube of 102 is 1,061,208.
Using a Calculator
To find the cube of 102 using a calculator, input the number 102 and use the cube function (if available) or multiply 102 × 102 × 102. This operation calculates the value of 102³, resulting in 1,061,208. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1, 0, followed by 2
Step 3: If the calculator has a cube function, press it to calculate 102³.
Step 4: If there is no cube function on the calculator, simply multiply 102 three times manually.
Step 5: The calculator will display 1,061,208.
Tips and Tricks for the Cube of 102
- 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 102
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, 102 × 102 and not 102 × 102 × 102. Always remember that 102³ = 102 × 102 × 102.
Solved Examples on Cube of 102
Problem 1
What is the cube and cube root of 102?
The cube of 102 is 1,061,208 and the cube root of 102 is approximately 4.649.
Explanation
First, let’s find the cube of 102.
We know that the cube of a number x, such that x³ = y
Where x is the given number, and y is the cubed value of that number
So, we get 102³ = 1,061,208 Next, we must find the cube root of 102
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 ∛102 ≈ 4.649
Hence the cube of 102 is 1,061,208 and the cube root of 102 is approximately 4.649.
Problem 2
If the side length of the cube is 102 cm, what is the volume?
The volume is 1,061,208 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 102 for the side length: V = 102³ = 1,061,208 cm³.
Problem 3
How much larger is 102³ than 100³?
102³ – 100³ = 61,208.
Explanation
First, find the cube of 102, which is 1,061,208.
Next, find the cube of 100, which is 1,000,000.
Now, find the difference between them using the subtraction method. 1,061,208 – 1,000,000 = 61,208
Therefore, 102³ is 61,208 larger than 100³.
Problem 4
If a cube with a side length of 102 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 102 cm is 1,061,208 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 102 means multiplying 102 by itself three times: 102 × 102 = 10,404, and then 10,404 × 102 = 1,061,208.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,061,208 cm³.
Problem 5
Estimate the cube of 101.9 using the cube of 102.
The cube of 101.9 is approximately 1,061,208.
Explanation
First, identify the cube of 102,
The cube of 102 is 102³ = 1,061,208.
Since 101.9 is only a tiny bit less than 102, the cube of 101.9 will be almost the same as the cube of 102.
The cube of 101.9 is approximately 1,061,208 because the difference between 101.9 and 102 is very small.
So, we can approximate the value as 1,061,208.
FAQs on Cube of 102
1.What are the perfect cubes up to 102?
2.How do you calculate 102³?
3.What is the meaning of 102³?
4.What is the cube root of 102?
5.Is 102 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 102?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube of 102?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube of 102
- 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.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
- Perfect Cube: A number that can be expressed as the cube of an integer is called a perfect cube.
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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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