Cube of 90
2026-02-28 13:59 Diff
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Last updated on August 5, 2025

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.

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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:

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Problem 1

What is the cube and cube root of 90?

Okay, lets begin

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.

Well explained 👍

Problem 2

If the side length of the cube is 90 cm, what is the volume?

Okay, lets begin

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.

Well explained 👍

Problem 3

How much larger is 90³ than 80³?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Estimate the cube of 89.9 using the cube of 90.

Okay, lets begin

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.

Well explained 👍

FAQs on Cube of 90

1.What are the perfect cubes up to 90?

The perfect cubes up to 90 are 1, 8, 27, and 64.

2.How do you calculate 90³?

To calculate 90³, use the multiplication method: 90 × 90 × 90, which equals 729,000.

3.What is the meaning of 90³?

90³ means 90 multiplied by itself three times, or 90 × 90 × 90.

4.What is the cube root of 90?

5.Is 90 a perfect cube?

No, 90 is not a perfect cube because no integer multiplied by itself three times equals 90.

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.