101 LearnersLast updated on June 3rd, 2025
Cube of 311
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used in while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 311.
Cube of 311
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 311 can be written as 3113, which is the exponential form. Or it can also be written in arithmetic form as 311 x 311 x 311.
How to Calculate the Value of Cube of 311
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.
- By Multiplication Method
- Using a Formula
- 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. 3113 = 311 x 311 x 311\
Step 2: You get 30,003,031 as the answer. Hence, the cube of 311 is 30,003,031.
Using a Formula (\(a^3\))
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 311 into two parts.
Let a = 300 and b = 11, so a + b = 311
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
Step 3: Calculate each term a3= 3003
3a2b = 3 x 3002 x 11
3ab2 = 3 x 300 x 112
b3 = 113
Step 4: Add all the terms together:
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(300 + 11)3 = 3003 + 3 x 3002 x 11 + 3 x 300 x 112 + 113
\(311^3 = 27,000,000 + 2,970,000 + 108,900 + 1,331\) \(311^3 = 30,003,031\) Step 5: Hence, the cube of 311 is 30,003,031.
Using a Calculator
To find the cube of 311 using a calculator, input the number 311 and use the cube function (if available) or multiply \(311 \times 311 \times 311\). This operation calculates the value of \(311^3\), resulting in 30,003,031. 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 1 and 1 Step 3: If the calculator has a cube function, press it to calculate \(311^3\). Step 4: If there is no cube function on the calculator, simply multiply 311 three times manually. Step 5: The calculator will display 30,003,031.
Tips and Tricks for the Cube of 311
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.
Common Mistakes to Avoid When Calculating the Cube of 311
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
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, \(311 \times 311\) and not \(311 \times 311 \times 311\). Always remember that \(311^3 = 311 \times 311 \times 311\).
Solved Examples on Cube of 311
Problem 1
What is the cube and cube root of 311?
The cube of 311 is 30,003,031 and the cube root of 311 is approximately 6.679.
Explanation
First, let’s find the cube of 311. We know that the cube of a number, such that \(x^3 = y\) Where \(x\) is the given number, and \(y\) is the cubed value of that number So, we get \(311^3 = 30,003,031\) Next, we must find the cube root of 311 We know that the cube root of a number ‘x’, such that \(\sqrt[3]{x} = y\) Where ‘x’ is the given number, and \(y\) is the cube root value of the number So, we get \(\sqrt[3]{311} \approx 6.679\) Hence the cube of 311 is 30,003,031 and the cube root of 311 is approximately 6.679.
Problem 2
If the side length of the cube is 311 cm, what is the volume?
The volume is 30,003,031 cm³.
Explanation
Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 311 for the side length: \(V = 311^3 = 30,003,031\) cm³.
Problem 3
How much larger is \(311^3\) than \(300^3\)?
\(311^3 - 300^3 = 2,973,031\).
Explanation
First, find the cube of \(311^3\), that is 30,003,031 Next, find the cube of \(300^3\), which is 27,000,000 Now, find the difference between them using the subtraction method. 30,003,031 - 27,000,000 = 2,973,031 Therefore, \(311^3\) is 2,973,031 larger than \(300^3\).
Problem 4
If a cube with a side length of 311 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 311 cm is 30,003,031 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 311 means multiplying 311 by itself three times: \(311 \times 311 = 96,721\), and then \(96,721 \times 311 = 30,003,031\). The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 30,003,031 cm³.
Problem 5
Estimate the cube of 310.5 using the cube of 311.
The cube of 310.5 is approximately 30,003,031.
Explanation
First, identify the cube of 311, The cube of 311 is \(311^3 = 30,003,031\). Since 310.5 is only a tiny bit less than 311, the cube of 310.5 will be almost the same as the cube of 311. The cube of 310.5 is approximately 30,003,031 because the difference between 310.5 and 311 is very small. So, we can approximate the value as 30,003,031.
FAQs on Cube of 311
1.What are the perfect cubes up to 311?
2.How do you calculate \(311^3\)?
3.What is the meaning of \(311^3\)?
4.What is the cube root of 311?
5.Is 311 a perfect cube?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube of 311?
8.How do technology and digital tools in Philippines support learning Algebra and Cube of 311?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube of 311
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, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. Perfect Cube: A number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because \(2^3 = 8\). Volume: The amount of space a 3-dimensional object occupies, often measured in cubic units such as cubic centimeters (cm³).
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Jaskaran Singh Saluja
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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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