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 103.
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 103 can be written as 103³, which is the exponential form.
Or it can also be written in arithmetic form as 103 × 103 × 103.
In order to determine whether a number is a cube number or not, we can use the following three methods: 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. 103³ = 103 × 103 × 103
Step 2: You get 1,092,727 as the answer.
Hence, the cube of 103 is 1,092,727.
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 103 into two parts. Let a = 100 and b = 3, so a + b = 103.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³.
Step 3: Calculate each term. a³ = 100³ 3a²b = 3 × 100² × 3 3ab² = 3 × 100 × 3² b³ = 3³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 3)³ = 100³ + 3 × 100² × 3 + 3 × 100 × 3² + 3³ 103³ = 1,000,000 + 90,000 + 2,700 + 27 103³ = 1,092,727
Step 5: Hence, the cube of 103 is 1,092,727.
To find the cube of 103 using a calculator, input the number 103 and use the cube function (if available) or multiply 103 × 103 × 103. This operation calculates the value of 103³, resulting in 1,092,727. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1 followed by 0, then 3.
Step 3: If the calculator has a cube function, press it to calculate 103³.
Step 4: If there is no cube function on the calculator, simply multiply 103 three times manually.
Step 5: The calculator will display 1,092,727.
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 103?
The cube of 103 is 1,092,727 and the cube root of 103 is approximately 4.674.
First, let’s find the cube of 103.
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 103³ = 1,092,727. Next, we must find the cube root of 103.
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 ∛103 ≈ 4.674.
Hence, the cube of 103 is 1,092,727 and the cube root of 103 is approximately 4.674.
If the side length of the cube is 103 cm, what is the volume?
The volume is 1,092,727 cm³.
Use the volume formula for a cube V = Side³.
Substitute 103 for the side length: V = 103³ = 1,092,727 cm³.
How much larger is 103³ than 100³?
103³ – 100³ = 92,727.
First find the cube of 103, which is 1,092,727.
Next, find the cube of 100, which is 1,000,000.
Now, find the difference between them using the subtraction method. 1,092,727 – 1,000,000 = 92,727.
Therefore, 103³ is 92,727 larger than 100³.
If a cube with a side length of 103 cm is compared to a cube with a side length of 50 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 103 cm is 1,092,727 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 103 means multiplying 103 by itself three times: 103 × 103 = 10,609, and then 10,609 × 103 = 1,092,727.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,092,727 cm³.
Estimate the cube of 102.9 using the cube of 103.
The cube of 102.9 is approximately 1,092,727.
First, identify the cube of 103.
The cube of 103 is 103³ = 1,092,727.
Since 102.9 is only a tiny bit less than 103, the cube of 102.9 will be almost the same as the cube of 103.
The cube of 102.9 is approximately 1,092,727 because the difference between 102.9 and 103 is very small.
So, we can approximate the value as 1,092,727.
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.