116 LearnersLast updated on May 30th, 2025
Cube of 225
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 cubes of 225.
Cube of 225
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 225 can be written as 225³, which is the exponential form.
Or it can also be written in arithmetic form as, 225 × 225 × 225.
How to Calculate the Value of Cube of 225
To determine 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 cube 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 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. 225³ = 225 × 225 × 225
Step 2: Calculate the result. You get 11,390,625 as the answer.
Hence, the cube of 225 is 11,390,625.
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 225 into two parts, as 200 and 25. Let a = 200 and b = 25, so a + b = 225
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ 3a²b = 3 × 200² × 25 3ab² = 3 × 200 × 25² b³ = 25³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (200 + 25)³ = 200³ + 3 × 200² × 25 + 3 × 200 × 25² + 25³ 225³ = 8,000,000 + 3,000,000 + 375,000 + 15,625 225³ = 11,390,625
Step 5: Hence, the cube of 225 is 11,390,625.
Using a Calculator
To find the cube of 225 using a calculator, input the number 225 and use the cube function (if available) or multiply 225 × 225 × 225. This operation calculates the value of 225³, resulting in 11,390,625. 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 2 and 5.
Step 3: If the calculator has a cube function, press it to calculate 225³.
Step 4: If there is no cube function on the calculator, simply multiply 225 three times manually.
Step 5: The calculator will display 11,390,625.
Tips and Tricks for the Cube of 225
- 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 225
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, 225 × 225 and not 225 × 225 × 225. Always remember that 225³ = 225 × 225 × 225.
Solved Examples on Cube of 225
Problem 1
What is the cube and cube root of 225?
The cube of 225 is 11,390,625 and the cube root of 225 is approximately 6.082.
Explanation
First, let’s find the cube of 225.
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 225³ = 11,390,625 Next, we must find the cube root of 225
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 ∛225 ≈ 6.082
Hence the cube of 225 is 11,390,625 and the cube root of 225 is approximately 6.082.
Problem 2
If the side length of the cube is 225 cm, what is the volume?
The volume is 11,390,625 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 225 for the side length: V = 225³ = 11,390,625 cm³.
Problem 3
How much larger is 225³ than 200³?
225³ – 200³ = 3,390,625.
Explanation
First, find the cube of 225³, that is 11,390,625
Next, find the cube of 200³, which is 8,000,000
Now, find the difference between them using the subtraction method. 11,390,625 – 8,000,000 = 3,390,625
Therefore, 225³ is 3,390,625 larger than 200³.
Problem 4
If a cube with a side length of 225 cm is compared to a cube with a side length of 25 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 225 cm is 11,390,625 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 225 means multiplying 225 by itself three times: 225 × 225 = 50,625, and then 50,625 × 225 = 11,390,625.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 11,390,625 cm³.
Problem 5
Estimate the cube of 224.9 using the cube of 225.
The cube of 224.9 is approximately 11,390,625.
Explanation
First, identify the cube of 225, The cube of 225 is 225³ = 11,390,625.
Since 224.9 is only a tiny bit less than 225, the cube of 224.9 will be almost the same as the cube of 225.
The cube of 224.9 is approximately 11,390,625 because the difference between 224.9 and 225 is very small.
So, we can approximate the value as 11,390,625.
FAQs on Cube of 225
1.What are the perfect cubes up to 225?
2.How do you calculate 225³?
3.What is the meaning of 225³?
4.What is the cube root of 225?
5.Is 225 a perfect cube?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Cube of 225?
8.How do technology and digital tools in Canada support learning Algebra and Cube of 225?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube of 225
- Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer. 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. For example, 8 is a perfect cube because it equals 2³.
- Volume: The amount of space occupied by a 3-dimensional object, often measured in cubic units. For a cube, it is calculated as side length cubed.
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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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