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Last updated on May 26th, 2025

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Cube of 361

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When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 361.

Cube of 361 for Omani Students
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Cube of 361

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 361 can be written as 361³, which is the exponential form. Or it can also be written in arithmetic form as 361 × 361 × 361.

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How to Calculate the Value of Cube of 361

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 (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. By Multiplication Method Using a Formula Using a Calculator

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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. 361³ = 361 × 361 × 361 Step 2: You get 47,087,881 as the answer. Hence, the cube of 361 is 47,087,881.

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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 361 into two parts, as 360 and 1. Let a = 360 and b = 1, so a + b = 361 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 360³ 3a²b = 3 × 360² × 1 3ab² = 3 × 360 × 1² b³ = 1³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (360 + 1)³ = 360³ + 3 × 360² × 1 + 3 × 360 × 1² + 1³ 361³ = 46,656,000 + 388,800 + 1,080 + 1 361³ = 47,087,881 Step 5: Hence, the cube of 361 is 47,087,881.

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Using a Calculator

To find the cube of 361 using a calculator, input the number 361 and use the cube function (if available) or multiply 361 × 361 × 361. This operation calculates the value of 361³, resulting in 47,087,881. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 3 followed by 6 and 1 Step 3: If the calculator has a cube function, press it to calculate 361³. Step 4: If there is no cube function on the calculator, simply multiply 361 three times manually. Step 5: The calculator will display 47,087,881.

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Tips and Tricks for the Cube of 361

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.

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Common Mistakes to Avoid When Calculating the Cube of 361

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:

Mistake 1

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Incorrect Multiplication

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Kids might multiply the numbers only twice. That is, 361 × 361 and not 361 × 361 × 361. Always remember that 361³ = 361 × 361 × 361.

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Solved Examples on Cube of 361

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Problem 1

What is the cube and cube root of 361?

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The cube of 361 is 47,087,881 and the cube root of 361 is approximately 7.123.

Explanation

First, let’s find the cube of 361. 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 361³ = 47,087,881 Next, we must find the cube root of 361 We know that the 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√361 = 7.123 Hence the cube of 361 is 47,087,881 and the cube root of 361 is approximately 7.123.

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Problem 2

If the side length of a cube is 361 cm, what is the volume?

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The volume is 47,087,881 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 361 for the side length: V = 361³ = 47,087,881 cm³.

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Problem 3

How much larger is 361³ than 360³?

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361³ - 360³ = 1,083.

Explanation

First find the cube of 361³, that is 47,087,881 Next, find the cube of 360³, which is 46,656,000 Now, find the difference between them using the subtraction method. 47,087,881 - 46,656,000 = 1,083 Therefore, 361³ is 1,083 larger than 360³.

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Problem 4

If a cube with a side length of 361 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 361 cm is 47,087,881 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 361 means multiplying 361 by itself three times: 361 × 361 = 130,321, and then 130,321 × 361 = 47,087,881. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 47,087,881 cm³.

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Problem 5

Estimate the cube of 360.9 using the cube of 361.

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The cube of 360.9 is approximately 47,087,881.

Explanation

First, identify the cube of 361, The cube of 361 is 361³ = 47,087,881. Since 360.9 is only a tiny bit less than 361, the cube of 360.9 will be almost the same as the cube of 361. The cube of 360.9 is approximately 47,087,881 because the difference between 360.9 and 361 is very small. So, we can approximate the value as 47,087,881.

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FAQs on Cube of 361

1.What are the perfect cubes up to 361?

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2.How do you calculate 361³?

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3.What is the meaning of 361³?

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4.What is the cube root of 361?

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5.Is 361 a perfect cube?

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6.How does learning Algebra help students in Oman make better decisions in daily life?

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7.How can cultural or local activities in Oman support learning Algebra topics such as Cube of 361?

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8.How do technology and digital tools in Oman support learning Algebra and Cube of 361?

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9.Does learning Algebra support future career opportunities for students in Oman?

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Important Glossaries for Cube of 361

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. Volume of a Cube: The measure of the space contained within a cube, calculated as the side length raised to the power of three. Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2.

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About BrightChamps in Oman

At BrightChamps, algebra is more than just digits—it’s a path to endless opportunities! We focus on helping children across Oman develop important math skills, like today’s focus on the Cube of 361, especially understanding cubes—in a fun, engaging, and easy-to-follow way. Whether your child is calculating how fast a roller coaster moves at Oman’s Dreamland Aqua Park, keeping track of scores at local sports events, or managing their allowance for the latest gadgets, mastering algebra gives them the confidence to meet everyday challenges. Our interactive lessons make math learning enjoyable and straightforward. Because children in Oman learn in diverse ways, we tailor our teaching to match each child’s style. From the vibrant city of Muscat to Oman’s natural landscapes, BrightChamps brings algebra to life, making it exciting and relatable throughout Oman. Let’s make cubes a fun part of every child’s math journey!
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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.

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Fun Fact

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

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