Last updated on June 3rd, 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 the cube of 221.
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 221 can be written as 221³, which is the exponential form. Or it can also be written in arithmetic form as, 221 × 221 × 221.
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.
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.
221³ = 221 × 221 × 221
Step 2: You get 10,795,061 as the answer.
Hence, the cube of 221 is 10,795,061.
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 221 into two parts, as 200 and 21. Let a = 200 and b = 21, so a + b = 221
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ , 3a²b = 3 × 200² × 21 , 3ab² = 3 × 200 × 21² , b³ = 21³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(200 + 21)³ = 200³ + 3 × 200² × 21 + 3 × 200 × 21² + 21³ 221³
= 8,000,000 + 2,520,000 + 264,600 + 9,261 221³ = 10,795,061
Step 5: Hence, the cube of 221 is 10,795,061.
To find the cube of 221 using a calculator, input the number 221 and use the cube function (if available) or multiply 221 × 221 × 221. This operation calculates the value of 221³, resulting in 10,795,061. 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 2, then 1
Step 3: If the calculator has a cube function, press it to calculate 221³.
Step 4: If there is no cube function on the calculator, simply multiply 221 three times manually.
Step 5: The calculator will display 10,795,061.
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 221?
The cube of 221 is 10,795,061, and the cube root of 221 is approximately 6.004.
First, let’s find the cube of 221.
We know that the cube of a number is such that x³ = y
Where x is the given number, and y is the cubed value of that number
So, we get 221³ = 10,795,061
Next, we must find the cube root of 221
We know that the cube root of a number ‘x’ is such that ∛x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ∛221 ≈ 6.004
Hence, the cube of 221 is 10,795,061, and the cube root of 221 is approximately 6.004.
If the side length of the cube is 221 cm, what is the volume?
The volume is 10,795,061 cm³.
Use the volume formula for a cube V = side³.
Substitute 221 for the side length: V = 221³ = 10,795,061 cm³.
How much larger is 221³ than 210³?
221³ – 210³ = 1,891,971.
First find the cube of 221, that is 10,795,061
Next, find the cube of 210, which is 9,103,090
Now, find the difference between them using the subtraction method.
10,795,061 – 9,103,090 = 1,891,971
Therefore, 221³ is 1,891,971 larger than 210³.
If a cube with a side length of 221 cm is compared to a cube with a side length of 21 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 221 cm is 10,795,061 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 221 means multiplying 221 by itself three times: 221 × 221 = 48,841, and then 48,841 × 221 = 10,795,061.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the larger cube is 10,795,061 cm³.
Estimate the cube of 220 using the cube of 221.
The cube of 220 is approximately 10,648,000.
First, identify the cube of 221, the cube of 221 is 221³ = 10,795,061.
Since 220 is very close to 221, the cube of 220 will be slightly less than the cube of 221.
The cube of 220 is approximately 10,648,000 because the difference between 220 and 221 is very small.
So, we can estimate the value as close to 10,648,000.
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.