Last updated on June 6th, 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 803.
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 803 can be written as 803³, which is the exponential form. Or it can also be written in arithmetic form as, 803 × 803 × 803.
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. 803³ = 803 × 803 × 803
Step 2: You get 518,763,427 as the answer. Hence, the cube of 803 is 518,763,427.
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 803 into two parts, as 800 and 3. Let a = 800 and b = 3, so a + b = 803
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 800³
3a²b = 3 × 800² × 3
3ab² = 3 × 800 × 3²
b³ = 3³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(800 + 3)³ = 800³ + 3 × 800² × 3 + 3 × 800 × 3² + 3³
803³ = 512,000,000 + 5,760,000 + 21,600 + 27
803³ = 518,763,427
Step 5: Hence, the cube of 803 is 518,763,427.
To find the cube of 803 using a calculator, input the number 803 and use the cube function (if available) or multiply 803 × 803 × 803. This operation calculates the value of 803³, resulting in 518,763,427. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 8 followed by 0 and 3
Step 3: If the calculator has a cube function, press it to calculate 803³.
Step 4: If there is no cube function on the calculator, simply multiply 803 three times manually.
Step 5: The calculator will display 518,763,427.
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 803?
The cube of 803 is 518,763,427 and the cube root of 803 is approximately 9.283.
First, let’s find the cube of 803.
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 803³ = 518,763,427.
Next, we must find the cube root of 803. 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, √803 ≈ 9.283.
Hence, the cube of 803 is 518,763,427 and the cube root of 803 is approximately 9.283.
If the side length of the cube is 803 cm, what is the volume?
The volume is 518,763,427 cm³.
Use the volume formula for a cube V = Side³.
Substitute 803 for the side length: V = 803³ = 518,763,427 cm³.
How much larger is 803³ than 703³?
803³ – 703³ = 398,508,127.
First find the cube of 803, which is 518,763,427.
Next, find the cube of 703, which is 120,255,300.
Now, find the difference between them using the subtraction method. 518,763,427 – 120,255,300 = 398,508,127.
Therefore, 803³ is 398,508,127 larger than 703³.
If a cube with a side length of 803 cm is compared to a cube with a side length of 103 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 803 cm is 518,763,427 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 803 means multiplying 803 by itself three times: 803 × 803 = 644,809, and then 644,809 × 803 = 518,763,427.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 518,763,427 cm³.
Estimate the cube of 802.5 using the cube of 803.
The cube of 802.5 is approximately 518,763,427.
First, identify the cube of 803.
The cube of 803 is 803³ = 518,763,427.
Since 802.5 is only a tiny bit less than 803, the cube of 802.5 will be almost the same as the cube of 803.
The cube of 802.5 is approximately 518,763,427 because the difference between 802.5 and 803 is very small.
So, we can approximate the value as 518,763,427.
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.