Cube of 310
2026-02-28 17:27 Diff
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Last updated on August 5, 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 310.

Cube of 310

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 310 can be written as 310³, which is the exponential form. Or it can also be written in arithmetic form as 310 × 310 × 310.

How to Calculate the Value of Cube of 310

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These methods help to cube numbers faster and easier without feeling confused or stuck while evaluating the answers.

  1. By Multiplication Method
  2. Using a Formula
  3. Using a Calculator

By Multiplication Method

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. 310³ = 310 × 310 × 310

Step 2: Calculate the product to get 29,791,000 as the answer.

Hence, the cube of 310 is 29,791,000.

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Using a Formula (a³)

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 310 into two parts. Let a = 300 and b = 10, so a + b = 310

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

Step 3: Calculate each term a³ = 300³ 3a²b = 3 × 300² × 10 3ab² = 3 × 300 × 10² b³ = 10³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(300 + 10)³ = 300³ + 3 × 300² × 10 + 3 × 300 × 10² + 10³

310³ = 27,000,000 + 2,700,000 + 90,000 + 1,000

310³ = 29,791,000

Step 5: Hence, the cube of 310 is 29,791,000.

Using a Calculator

To find the cube of 310 using a calculator, input the number 310 and use the cube function (if available) or multiply 310 × 310 × 310. This operation calculates the value of 310³, resulting in 29,791,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input 310.

Step 3: If the calculator has a cube function, press it to calculate 310³.

Step 4: If there is no cube function on the calculator, simply multiply 310 three times manually.

Step 5: The calculator will display 29,791,000.

Tips and Tricks for the Cube of 310

  • 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.

Common Mistakes to Avoid When Calculating the Cube of 310

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:

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Problem 1

What is the cube and cube root of 310?

Okay, lets begin

The cube of 310 is 29,791,000 and the cube root of 310 is approximately 6.7109.

Explanation

First, let’s find the cube of 310.

We know that 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 310³ = 29,791,000

Next, we must find the cube root of 310 We know that cube root of a number ‘x’, such that ³√x = y Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ³√310 ≈ 6.7109

Hence the cube of 310 is 29,791,000 and the cube root of 310 is approximately 6.7109.

Well explained 👍

Problem 2

If the side length of the cube is 310 cm, what is the volume?

Okay, lets begin

The volume is 29,791,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 310 for the side length: V = 310³ = 29,791,000 cm³.

Well explained 👍

Problem 3

How much larger is 310³ than 300³?

Okay, lets begin

310³ – 300³ = 2,791,000.

Explanation

First find the cube of 310³, that is 29,791,000

Next, find the cube of 300³, which is 27,000,000

Now, find the difference between them using the subtraction method.

29,791,000 – 27,000,000 = 2,791,000

Therefore, 310³ is 2,791,000 larger than 300³.

Well explained 👍

Problem 4

If a cube with a side length of 310 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 310 cm is 29,791,000 cm³

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 310 means multiplying 310 by itself three times: 310 × 310 = 96,100, and then 96,100 × 310 = 29,791,000.

The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.

Therefore, the volume of the cube is 29,791,000 cm³.

Well explained 👍

Problem 5

Estimate the cube of 309.9 using the cube of 310.

Okay, lets begin

The cube of 309.9 is approximately 29,791,000.

Explanation

First, identify the cube of 310, The cube of 310 is 310³ = 29,791,000.

Since 309.9 is only a tiny bit less than 310, the cube of 309.9 will be almost the same as the cube of 310.

The cube of 309.9 is approximately 29,791,000 because the difference between 309.9 and 310 is very small.

So, we can approximate the value as 29,791,000.

Well explained 👍

FAQs on Cube of 310

1.What are the perfect cubes up to 310?

The perfect cubes up to 310 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate 310³?

To calculate 310³, use the multiplication method, 310 × 310 × 310, which equals 29,791,000.

3.What is the meaning of 310³?

310³ means 310 multiplied by itself three times, or 310 × 310 × 310.

4.What is the cube root of 310?

The cube root of 310 is approximately 6.7109.

5.Is 310 a perfect cube?

No, 310 is not a perfect cube because no integer multiplied by itself three times equals 310.

Important Glossaries for Cube of 310

  • Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
  • Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
  • Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
  • Perfect Cube: A number that can be expressed as the cube of an integer.
  • Volume: The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great.

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Jaskaran Singh Saluja

About the Author

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.