Last updated on May 30th, 2025
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 224.
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 224 can be written as 224³, which is the exponential form.
Or it can also be written in arithmetic form as, 224 × 224 × 224.
In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These methods will help kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.
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. 224³ = 224 × 224 × 224
Step 2: You get 11,238,784 as the answer.
Hence, the cube of 224 is 11,238,784.
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 224 into two parts, as 200 and 24. Let a = 200 and b = 24, so a + b = 224
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ 3a²b = 3 × 200² × 24 3ab² = 3 × 200 × 24² b³ = 24³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (200 + 24)³ = 200³ + 3 × 200² × 24 + 3 × 200 × 24² + 24³ 224³ = 8,000,000 + 2,880,000 + 345,600 + 13,824 224³ = 11,238,784
Step 5: Hence, the cube of 224 is 11,238,784.
To find the cube of 224 using a calculator, input the number 224 and use the cube function (if available) or multiply 224 × 224 × 224. This operation calculates the value of 224³, resulting in 11,238,784. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2, 2, and 4
Step 3: If the calculator has a cube function, press it to calculate 224³.
Step 4: If there is no cube function on the calculator, simply multiply 224 three times manually.
Step 5: The calculator will display 11,238,784.
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:
What is the cube and cube root of 224?
The cube of 224 is 11,238,784, and the cube root of 224 is approximately 6.000.
First, let’s find the cube of 224.
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 224³ = 11,238,784.
Next, we must find the cube root of 224.
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 ∛224 ≈ 6.000.
Hence, the cube of 224 is 11,238,784, and the cube root of 224 is approximately 6.000.
If the side length of the cube is 224 cm, what is the volume?
The volume is 11,238,784 cm³.
Use the volume formula for a cube V = Side³.
Substitute 224 for the side length: V = 224³ = 11,238,784 cm³.
How much larger is 224³ than 200³?
224³ – 200³ = 3,238,784.
First, find the cube of 224³, which is 11,238,784.
Next, find the cube of 200³, which is 8,000,000.
Now, find the difference between them using the subtraction method. 11,238,784 – 8,000,000 = 3,238,784.
Therefore, 224³ is 3,238,784 larger than 200³.
If a cube with a side length of 224 cm is compared to a cube with a side length of 24 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 224 cm is 11,238,784 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 224 means multiplying 224 by itself three times: 224 × 224 = 50,176, and 50,176 × 224 = 11,238,784.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 11,238,784 cm³.
Estimate the cube of 223.9 using the cube of 224.
The cube of 223.9 is approximately 11,238,784.
First, identify the cube of 224.
The cube of 224 is 224³ = 11,238,784.
Since 223.9 is only a tiny bit less than 224, the cube of 223.9 will be almost the same as the cube of 224.
The cube of 223.9 is approximately 11,238,784 because the difference between 223.9 and 224 is very small.
So, we can approximate the value as 11,238,784.
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.
: He loves to play the quiz with kids through algebra to make kids love it.