101 LearnersLast updated on June 3rd, 2025
Cube of 280
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is useful when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 280.
Cube of 280
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 280 can be written as 280³, which is the exponential form.
Or it can also be written in arithmetic form as 280 × 280 × 280.
How to Calculate the Value of Cube of 280
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 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. 280³ = 280 × 280 × 280
Step 2: You get 21,952,000 as the answer. Hence, the cube of 280 is 21,952,000.
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 280 into two parts, as a and b. Let a = 200 and b = 80, so a + b = 280
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ 3a²b = 3 × 200² × 80 3ab² = 3 × 200 × 80² b³ = 80³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (200 + 80)³ = 200³ + 3 × 200² × 80 + 3 × 200 × 80² + 80³ 280³ = 8,000,000 + 9,600,000 + 3,840,000 + 512,000 280³ = 21,952,000
Step 5: Hence, the cube of 280 is 21,952,000.
Using a Calculator
To find the cube of 280 using a calculator, input the number 280 and use the cube function (if available) or multiply 280 × 280 × 280. This operation calculates the value of 280³, resulting in 21,952,000. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2, then 8, followed by 0.
Step 3: If the calculator has a cube function, press it to calculate 280³.
Step 4: If there is no cube function on the calculator, simply multiply 280 three times manually.
Step 5: The calculator will display 21,952,000.
Tips and Tricks for the Cube of 280
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 280
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, 280 × 280 and not 280 × 280 × 280. Always remember that 280³ = 280 × 280 × 280.
Solved Examples on Cube of 280
Problem 1
What is the cube and cube root of 280?
The cube of 280 is 21,952,000 and the cube root of 280 is approximately 6.556.
Explanation
First, let’s find the cube of 280.
We know that 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 280³ = 21,952,000 Next, we must find the cube root of 280.
We know that 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 ∛280 ≈ 6.556
Hence, the cube of 280 is 21,952,000 and the cube root of 280 is approximately 6.556.
Problem 2
If the side length of the cube is 280 cm, what is the volume?
The volume is 21,952,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 280 for the side length: V = 280³ = 21,952,000 cm³.
Problem 3
How much larger is 280³ than 200³?
280³ – 200³ = 13,952,000.
Explanation
First, find the cube of 280³, that is 21,952,000.
Next, find the cube of 200³, which is 8,000,000.
Now, find the difference between them using the subtraction method. 21,952,000 – 8,000,000 = 13,952,000
Therefore, 280³ is 13,952,000 larger than 200³.
Problem 4
If a cube with a side length of 280 cm is compared to a cube with a side length of 80 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 280 cm is 21,952,000 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 280 means multiplying 280 by itself three times: 280 × 280 = 78,400, and then 78,400 × 280 = 21,952,000.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 21,952,000 cm³.
Problem 5
Estimate the cube of 279.5 using the cube of 280.
The cube of 279.5 is approximately 21,952,000.
Explanation
First, identify the cube of 280,
The cube of 280 is 280³ = 21,952,000.
Since 279.5 is only a tiny bit less than 280, the cube of 279.5 will be almost the same as the cube of 280.
The cube of 279.5 is approximately 21,952,000 because the difference between 279.5 and 280 is very small.
So, we can approximate the value as 21,952,000.
FAQs on Cube of 280
1.What are the perfect cubes up to 280?
2.How do you calculate 280³?
3.What is the meaning of 280³?
4.What is the cube root of 280?
5.Is 280 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 280?
8.How do technology and digital tools in United States support learning Algebra and Cube of 280?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 280
- 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 is called a perfect cube.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of its side length.
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Jaskaran Singh Saluja
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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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