Last updated on May 28th, 2025
When a number is multiplied by itself three times, the resultant number is called the cube of that number. Cubing is used when comparing the volumes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 478.
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 478 can be written as 478³, which is the exponential form. Or it can also be written in arithmetic form as, 478 × 478 × 478.
To check whether a number is a cube number or not, we can use the following methods: multiplication method, a factor formula (a³), or by using a calculator. These methods will help compute the cube of numbers faster and easier without confusion.
The multiplication method is a mathematical process used to find the product of numbers by repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number. 478³ = 478 × 478 × 478
Step 2: You get 109,938,952 as the answer. Hence, the cube of 478 is 109,938,952.
The formula (a + b)³ is a binomial formula used to find the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.
Step 1: Split the number 478 into two parts, such as a and b. Let a = 400 and b = 78, so a + b = 478
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 400³
3a²b = 3 × 400² × 78
3ab² = 3 × 400 × 78²
b³ = 78³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(400 + 78)³ = 400³ + 3 × 400² × 78 + 3 × 400 × 78² + 78³
478³ = 64,000,000 + 37,440,000 + 7,286,400 + 474,552
478³ = 109,938,952
Step 5: Hence, the cube of 478 is 109,938,952.
To find the cube of 478 using a calculator, input the number 478 and use the cube function (if available) or multiply 478 × 478 × 478. This operation calculates the value of 478³, resulting in 109,938,952. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 478
Step 3: If the calculator has a cube function, press it to calculate 478³.
Step 4: If there is no cube function, simply multiply 478 three times manually.
Step 5: The calculator will display 109,938,952.
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five major mistakes that might occur:
What is the cube and cube root of 478?
The cube of 478 is 109,938,952, and the cube root of 478 is approximately 7.798.
First, let’s find the cube of 478.
We know that the cube of a number x, such that x³ = y Where x is the given number, and y is the cubed value of that number
So, we get 478³ = 109,938,952
Next, we must find the cube root of 478 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 ∛478 ≈ 7.798
Hence, the cube of 478 is 109,938,952, and the cube root of 478 is approximately 7.798.
If the side length of a cube is 478 cm, what is the volume?
The volume is 109,938,952 cm³.
Use the volume formula for a cube V = Side³.
Substitute 478 for the side length: V = 478³ = 109,938,952 cm³.
How much larger is 478³ than 300³?
478³ – 300³ = 76,938,952.
First, find the cube of 478, which is 109,938,952.
Next, find the cube of 300, which is 27,000,000.
Now, find the difference between them using the subtraction method.
109,938,952 – 27,000,000 = 76,938,952
Therefore, 478³ is 76,938,952 larger than 300³.
If a cube with a side length of 478 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 478 cm is 109,938,952 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 478 means multiplying 478 by itself three times: 478 × 478 = 228,484, and then 228,484 × 478 = 109,938,952.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 109,938,952 cm³.
Estimate the cube of 477.9 using the cube of 478.
The cube of 477.9 is approximately 109,938,952.
First, identify the cube of 478, The cube of 478 is 478³ = 109,938,952.
Since 477.9 is only a tiny bit less than 478, the cube of 477.9 will be almost the same as the cube of 478.
The cube of 477.9 is approximately 109,938,952 because the difference between 477.9 and 478 is very small.
So, we can approximate the value as 109,938,952.
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.