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 462.
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 462 can be written as 462³, which is the exponential form. Or it can also be written in arithmetic form as, 462 × 462 × 462.
In order to check 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.
462³ = 462 × 462 × 462
Step 2: You get 98,304,328 as the answer.
Hence, the cube of 462 is 98,304,328.
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 462 into two parts.
Let a = 460 and b = 2, so a + b = 462
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 460³
3a²b = 3 × 460² × 2
3ab² = 3 × 460 × 2²
b³ = 2³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(460 + 2)³ = 460³ + 3 × 460² × 2 + 3 × 460 × 2² + 2³
462³ = 97,336,000 + 1,267,200 + 5,520 + 8
462³ = 98,608,728
Step 5: Hence, the cube of 462 is 98,608,728.
To find the cube of 462 using a calculator, input the number 462 and use the cube function (if available) or multiply 462 × 462 × 462. This operation calculates the value of 462³, resulting in 98,608,728. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 4, 6, 2
Step 3: If the calculator has a cube function, press it to calculate 462³.
Step 4: If there is no cube function on the calculator, simply multiply 462 three times manually.
Step 5: The calculator will display 98,608,728.
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 462?
The cube of 462 is 98,608,728 and the cube root of 462 is approximately 7.773.
First, let’s find the cube of 462.
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 462³ = 98,608,728.
Next, we must find the cube root of 462. 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 ∛462 ≈ 7.773
Hence the cube of 462 is 98,608,728 and the cube root of 462 is approximately 7.773.
If the side length of a cube is 462 cm, what is the volume?
The volume is 98,608,728 cm³.
Use the volume formula for a cube V = Side³.
Substitute 462 for the side length: V = 462³ = 98,608,728 cm³.
How much larger is 462³ than 460³?
462³ – 460³ = 1,272,728.
First, find the cube of 462, that is 98,608,728.
Next, find the cube of 460, which is 97,336,000.
Now, find the difference between them using the subtraction method.
98,608,728 – 97,336,000 = 1,272,728
Therefore, 462³ is 1,272,728 larger than 460³.
If a cube with a side length of 462 cm is compared to a cube with a side length of 2 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 462 cm is 98,608,728 cm³
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 462 means multiplying 462 by itself three times: 462 × 462 = 213,444, and then 213,444 × 462 = 98,608,728.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 98,608,728 cm³.
Estimate the cube of 461.9 using the cube of 462.
The cube of 461.9 is approximately 98,608,728.
First, identify the cube of 462.
The cube of 462 is 462³ = 98,608,728.
Since 461.9 is only a tiny bit less than 462, the cube of 461.9 will be almost the same as the cube of 462.
The cube of 461.9 is approximately 98,608,728 because the difference between 461.9 and 462 is very small.
So, we can approximate the value as 98,608,728.
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.