119 LearnersLast updated on May 26th, 2025
Cube of 180
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 180.
Cube of 180
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 by itself three times results in a negative number.
The cube of 180 can be written as 180³, which is the exponential form. Or it can also be written in arithmetic form as, 180 × 180 × 180.
How to Calculate the Value of Cube of 180
In order to check whether a number is a cube number or not, we can use the following three methods, such as the 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 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. 180³ = 180 × 180 × 180
Step 2: You get 5,832,000 as the answer. Hence, the cube of 180 is 5,832,000.
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 180 into two parts, as 160 and 20. Let a = 160 and b = 20, so a + b = 180
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 160³ 3a²b = 3 × 160² × 20 3ab² = 3 × 160 × 20² b³ = 20³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(160 + 20)³ = 160³ + 3 × 160² × 20 + 3 × 160 × 20² + 20³
180³ = 4,096,000 + 1,536,000 + 192,000 + 8,000
180³ = 5,832,000
Step 5: Hence, the cube of 180 is 5,832,000.
Using a Calculator
To find the cube of 180 using a calculator, input the number 180 and use the cube function (if available) or multiply 180 × 180 × 180. This operation calculates the value of 180³, resulting in 5,832,000. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 180
Step 3: If the calculator has a cube function, press it to calculate 180³.
Step 4: If there is no cube function on the calculator, simply multiply 180 three times manually.
Step 5: The calculator will display 5,832,000.
Tips and Tricks for the Cube of 180
- 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 180
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, 180 × 180 and not 180 × 180 × 180. Always remember that 180³ = 180 × 180 × 180.
Solved Examples on Cube of 180
Problem 1
What is the cube and cube root of 180?
The cube of 180 is 5,832,000 and the cube root of 180 is approximately 5.643.
Explanation
First, let’s find the cube of 180.
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 180³ = 5,832,000
Next, we must find the cube root of 180 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 ∛180 ≈ 5.643
Hence the cube of 180 is 5,832,000 and the cube root of 180 is approximately 5.643.
Problem 2
If the side length of the cube is 180 cm, what is the volume?
The volume is 5,832,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 180 for the side length: V = 180³ = 5,832,000 cm³.
Problem 3
How much larger is 180³ than 160³?
180³ – 160³ = 1,736,000.
Explanation
First find the cube of 180³, which is 5,832,000
Next, find the cube of 160³, which is 4,096,000
Now, find the difference between them using the subtraction method.
5,832,000 – 4,096,000 = 1,736,000
Therefore, 180³ is 1,736,000 larger than 160³.
Problem 4
If a cube with a side length of 180 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 180 cm is 5,832,000 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 180 means multiplying 180 by itself three times: 180 × 180 = 32,400, and then 32,400 × 180 = 5,832,000.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 5,832,000 cm³.
Problem 5
Estimate the cube of 179.9 using the cube of 180.
The cube of 179.9 is approximately 5,832,000.
Explanation
First, identify the cube of 180, The cube of 180 is 180³ = 5,832,000.
Since 179.9 is only a tiny bit less than 180, the cube of 179.9 will be almost the same as the cube of 180.
The cube of 179.9 is approximately 5,832,000 because the difference between 179.9 and 180 is very small.
So, we can approximate the value as 5,832,000.
FAQs on Cube of 180
1.What are the perfect cubes up to 180?
2.How do you calculate 180³?
3.What is the meaning of 180³?
4.What is the cube root of 180?
5.Is 180 a perfect cube?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of 180?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 180?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube of 180
- 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 equals 8.
- Perfect Cube: A number that can be expressed as the product of three identical integers.
- Volume of a Cube: The amount of space inside a cube, calculated as the cube of its side length, Side³.
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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
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