100 LearnersLast updated on June 3rd, 2025
Cube of 200
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 cubes of 200.
Cube of 200
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 200 can be written as 200³, which is the exponential form. Or it can also be written in arithmetic form as 200 × 200 × 200.
How to Calculate the Value of Cube of 200
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
- 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.
200³ = 200 × 200 × 200
Step 2: You get 8,000,000 as the answer.
Hence, the cube of 200 is 8,000,000.
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 200 into two parts, as and . Let a = 150 and b = 50, so a + b = 200
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 150³ , 3a²b = 3 × 150² × 50 , 3ab² = 3 × 150 × 50² , b³ = 50³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(150 + 50)³ = 150³ + 3 × 150² × 50 + 3 × 150 × 50² + 50³ 200³
= 3,375,000 + 1,125,000 + 1,125,000 + 125,000 200³ = 8,000,000
Step 5: Hence, the cube of 200 is 8,000,000.
Using a Calculator
To find the cube of 200 using a calculator, input the number 200 and use the cube function (if available) or multiply 200 × 200 × 200. This operation calculates the value of 200³, resulting in 8,000,000. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2 followed by 0 and 0
Step 3: If the calculator has a cube function, press it to calculate 200³.
Step 4: If there is no cube function on the calculator, simply multiply 200 three times manually.
Step 5: The calculator will display 8,000,000.
Tips and Tricks for the Cube of 200
- 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 200
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, 200 × 200 and not 200 × 200 × 200. Always remember that 200³ = 200 × 200 × 200.
Solved Examples on Cube of 200
Problem 1
What is the cube and cube root of 200?
The cube of 200 is 8,000,000 and the cube root of 200 is approximately 5.848.
Explanation
First, let’s find the cube of 200. We know that the cube of a number is such that x³ = y, where x is the given number, and y is the cubed value of that number.
So, we get 200³ = 8,000,000. Next, we must find the cube root of 200.
We know that the cube root of a number x is such that ∛x = y, where x is the given number, and y is the cube root value of the number.
So, we get ∛200 ≈ 5.848.
Hence, the cube of 200 is 8,000,000 and the cube root of 200 is approximately 5.848.
Problem 2
If the side length of the cube is 200 cm, what is the volume?
The volume is 8,000,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 200 for the side length: V = 200³ = 8,000,000 cm³.
Problem 3
How much larger is 200³ than 100³?
200³ – 100³ = 7,900,000.
Explanation
First, find the cube of 200³, which is 8,000,000.
Next, find the cube of 100³, which is 1,000,000.
Now, find the difference between them using the subtraction method.
8,000,000 – 1,000,000 = 7,000,000.
Therefore, 200³ is 7,000,000 larger than 100³.
Problem 4
If a cube with a side length of 200 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 200 cm is 8,000,000 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 200 means multiplying 200 by itself three times: 200 × 200 = 40,000, and then 40,000 × 200 = 8,000,000.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 8,000,000 cm³.
Problem 5
Estimate the cube 199.9 using the cube of 200.
The cube of 199.9 is approximately 8,000,000.
Explanation
First, identify the cube of 200, The cube of 200 is 200³ = 8,000,000.
Since 199.9 is only a tiny bit less than 200, the cube of 199.9 will be almost the same as the cube of 200.
The cube of 199.9 is approximately 8,000,000 because the difference between 199.9 and 200 is very small.
So, we can approximate the value as 8,000,000.
FAQs on Cube of 200
1.What are the perfect cubes up to 200?
2.How do you calculate 200³?
3.What is the meaning of 200³?
4.What is the cube root of 200?
5.Is 200 a perfect cube?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube of 200?
8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 200?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for Cube of 200
- 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.
- 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. Examples include 1, 8, 27, etc.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
