Last updated on June 2nd, 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 503.
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 503 can be written as 5033, which is the exponential form. Or it can also be written in arithmetic form as, 503 × 503 × 503.
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 (a^3), 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.
5033 = 503 × 503 × 503
Step 2: Calculate the product to get 127,512,027 as the answer.
Hence, the cube of 503 is 127,512,027.
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 503 into two parts, say 500 and 3.
Let a = 500 and b = 3, so a + b = 503
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
Step 3: Calculate each term a3 = 5003 , 3a2b = 3 × 5002 × 3 , 3ab2 = 3 × 500 × 32 , b3 = 33
Step 4: Add all the terms together:
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(500 + 3)3 = 5003 + 3 × 5002 × 3 + 3 × 500 × 32 + 33
5033 = 125,000,000 + 2,250,000 + 13,500 + 27 5033
= 127,512,027
Step 5: Hence, the cube of 503 is 127,512,027.
To find the cube of 503 using a calculator, input the number 503 and use the cube function (if available) or multiply 503 × 503 × 503. This operation calculates the value of 503^3, resulting in 127,512,027. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 5, 0, and 3
Step 3: If the calculator has a cube function, press it to calculate 5033.
Step 4: If there is no cube function on the calculator, simply multiply 503 three times manually.
Step 5: The calculator will display 127,512,027.
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 503?
The cube of 503 is 127,512,027 and the cube root of 503 is approximately 7.938.
First, let’s find the cube of 503.
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 5033 = 127,512,027.
Next, we must find the cube root of 503. 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.
Using a calculator, ∛503 ≈ 7.938.
Hence, the cube of 503 is 127,512,027 and the cube root of 503 is approximately 7.938.
If the side length of a cube is 503 cm, what is the volume?
The volume is 127,512,027 cm3.
Use the volume formula for a cube V = Side3.
Substitute 503 for the side length: V = 5033 = 127,512,027 cm3.
How much larger is 503^3 than 403^3?
503^3 – 403^3 = 65,512,027.
First, find the cube of 503, which is 127,512,027.
Next, find the cube of 403, which is 64,000,000.
Now, find the difference between them using the subtraction method.
127,512,027 – 64,000,000 = 65,512,027.
Therefore, 5033 is 65,512,027 larger than 4033.
If a cube with a side length of 503 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 503 cm is 127,512,027 cm3 and is much larger compared to the cube with a side length of 100 cm.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 503 means multiplying 503 by itself three times:
503 × 503 × 503 = 127,512,027.
The unit of volume is cubic centimeters (cm3), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 127,512,027 cm3.
Estimate the cube of 502.9 using the cube of 503.
The cube of 502.9 is approximately 127,512,027.
First, identify the cube of 503.
The cube of 503 is 5033 = 127,512,027.
Since 502.9 is only a tiny bit less than 503, the cube of 502.9 will be almost the same as the cube of 503.
The cube of 502.9 is approximately 127,512,027 because the difference between 502.9 and 503 is very small.
So, we can approximate the value as 127,512,027.
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.