115 LearnersLast updated on May 30th, 2025
Cube of 90
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 90.
Cube of 90
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 90 can be written as 90³, which is the exponential form.
Or it can also be written in arithmetic form as 90 × 90 × 90.
How to Calculate the Value of Cube of 90
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 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. 90³ = 90 × 90 × 90
Step 2: You get 729,000 as the answer.
Hence, the cube of 90 is 729,000.
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 90 into two parts. Let a = 80 and b = 10, so a + b = 90
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 80³ 3a²b = 3 × 80² × 10 3ab² = 3 × 80 × 10² b³ = 10³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (80 + 10)³ = 80³ + 3 × 80² × 10 + 3 × 80 × 10² + 10³ 90³ = 512,000 + 192,000 + 24,000 + 1,000 90³ = 729,000
Step 5: Hence, the cube of 90 is 729,000.
Using a Calculator
To find the cube of 90 using a calculator, input the number 90 and use the cube function (if available) or multiply 90 × 90 × 90. This operation calculates the value of 90³, resulting in 729,000. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 9 followed by 0
Step 3: If the calculator has a cube function, press it to calculate 90³.
Step 4: If there is no cube function on the calculator, simply multiply 90 three times manually.
Step 5: The calculator will display 729,000.
Tips and Tricks for the Cube of 90
- 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 90
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, 90 × 90 and not 90 × 90 × 90. Always remember that 90³ = 90 × 90 × 90.
Solved Examples on Cube of 90
Problem 1
What is the cube and cube root of 90?
The cube of 90 is 729,000, and the cube root of 90 is 4.481.
Explanation
First, let’s find the cube of 90.
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 90³ = 729,000 Next, we must find the cube root of 90
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√90 ≈ 4.481
Hence the cube of 90 is 729,000, and the cube root of 90 is approximately 4.481.
Problem 2
If the side length of the cube is 90 cm, what is the volume?
The volume is 729,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 90 for the side length: V = 90³ = 729,000 cm³.
Problem 3
How much larger is 90³ than 80³?
90³ – 80³ = 217,000.
Explanation
First, find the cube of 90³, that is 729,000
Next, find the cube of 80³, which is 512,000
Now, find the difference between them using the subtraction method. 729,000 – 512,000 = 217,000
Therefore, 90³ is 217,000 larger than 80³.
Problem 4
If a cube with a side length of 90 cm is compared to a cube with a side length of 20 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 90 cm is 729,000 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 90 means multiplying 90 by itself three times: 90 × 90 = 8,100, and then 8,100 × 90 = 729,000.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 729,000 cm³.
Problem 5
Estimate the cube of 89.9 using the cube of 90.
The cube of 89.9 is approximately 729,000.
Explanation
First, identify the cube of 90,
The cube of 90 is 90³ = 729,000.
Since 89.9 is only a tiny bit less than 90, the cube of 89.9 will be almost the same as the cube of 90.
The cube of 89.9 is approximately 729,000 because the difference between 89.9 and 90 is very small.
So, we can approximate the value as 729,000.
FAQs on Cube of 90
1.What are the perfect cubes up to 90?
2.How do you calculate 90³?
3.What is the meaning of 90³?
4.What is the cube root of 90?
5.Is 90 a perfect cube?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 90?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 90?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 90
- 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, equaling 8.
- Perfect Cube: A number that can be expressed as the product of three equal integers.
- Cube Root: The number that produces a given number when cubed. For example, the cube root of 8 is 2 because 2³ = 8.
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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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