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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 413.
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 413 can be written as 4133, which is the exponential form.
Or it can also be written in arithmetic form as, 413 × 413 × 413.
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 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. 4133 = 413 × 413 × 413
Step 2: You get 70,381,997 as the answer. Hence, the cube of 413 is 70,381,997.
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 413 into two parts, as 400 and 13. Let a = 400 and b = 13, so a + b = 413
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
Step 3: Calculate each term a^3 = 400^3 3a^2b = 3 × 400^2 × 13 3ab^2 = 3 × 400 × 13^2 b^3 = 13^3
Step 4: Add all the terms together: (a + b)^3 = a3 + 3a2b + 3ab2 + b3 (400 + 13)3 = 4003 + 3 × 4002 × 13 + 3 × 400 × 132 + 133 4133 = 64,000,000 + 6,240,000 + 202,800 + 2,197 4133 = 70,381,997
Step 5: Hence, the cube of 413 is 70,381,997.
To find the cube of 413 using a calculator, input the number 413 and use the cube function (if available) or multiply 413 × 413 × 413. This operation calculates the value of 413^3, resulting in 70,381,997. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 413
Step 3: If the calculator has a cube function, press it to calculate 413^3.
Step 4: If there is no cube function on the calculator, simply multiply 413 three times manually.
Step 5: The calculator will display 70,381,997.
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.
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 413?
The cube of 413 is 70,381,997 and the cube root of 413 is approximately 7.4485.
First, let’s find the cube of 413.
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 4133 = 70,381,997.
Next, we must find the cube root of 413.
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 ∛413 ≈ 7.4485.
Hence, the cube of 413 is 70,381,997 and the cube root of 413 is approximately 7.4485.
If the side length of the cube is 413 cm, what is the volume?
The volume is 70,381,997 cm^3.
Use the volume formula for a cube V = Side3.
Substitute 413 for the side length: V = 4133 = 70,381,997 cm3.
How much larger is 413^3 than 400^3?
4133 – 4003 = 6,381,997.
First, find the cube of 4133, which is 70,381,997.
Next, find the cube of 4003, which is 64,000,000.
Now, find the difference between them using the subtraction method. 70,381,997 – 64,000,000 = 6,381,997.
Therefore, 4133 is 6,381,997 larger than 4003.
If a cube with a side length of 413 cm is compared to a cube with a side length of 13 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 413 cm is 70,381,997 cm^3.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 413 means multiplying 413 by itself three times: 413 × 413 = 170,569, and then 170,569 × 413 = 70,381,997.
The unit of volume is cubic centimeters (cm3) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 70,381,997 cm3.
Estimate the cube of 412.9 using the cube of 413.
The cube of 412.9 is approximately 70,381,997.
First, identify the cube of 413.
The cube of 413 is 4133 = 70,381,997.
Since 412.9 is only a tiny bit less than 413, the cube of 412.9 will be almost the same as the cube of 413.
The cube of 412.9 is approximately 70,381,997 because the difference between 412.9 and 413 is very small.
So, we can approximate the value as 70,381,997.
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.