Cube of -11
2026-02-28 11:42 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-minus-11

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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 -11.

Cube of -11

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 multiplying a negative number by itself three times results in a negative number. The cube of -11 can be written as (-11)^3, which is the exponential form. Or it can also be written in arithmetic form as (-11) × (-11) × (-11).

How to Calculate the Value of Cube of -11

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, factor formula (a^3), or by using a calculator. These three methods will help students 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 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. (-11)^3 = (-11) × (-11) × (-11) Step 2: You get -1,331 as the answer. Hence, the cube of -11 is -1,331.

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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 a^3 + 3a^2b + 3ab^2 + b^3. Step 1: Split the number -11 into two parts, as -10 and -1. Let a = -10 and b = -1, so a + b = -11 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-10)^3 3a^2b = 3 × (-10)^2 × (-1) 3ab^2 = 3 × (-10) × (-1)^2 b^3 = (-1)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-10 + -1)^3 = (-10)^3 + 3 × (-10)^2 × (-1) + 3 × (-10) × (-1)^2 + (-1)^3 (-11)^3 = -1,000 - 300 - 30 - 1 (-11)^3 = -1,331 Step 5: Hence, the cube of -11 is -1,331.

Using a Calculator

To find the cube of -11 using a calculator, input the number -11 and use the cube function (if available) or multiply (-11) × (-11) × (-11). This operation calculates the value of (-11)^3, resulting in -1,331. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -11 Step 3: If the calculator has a cube function, press it to calculate (-11)^3. Step 4: If there is no cube function on the calculator, simply multiply -11 three times manually. Step 5: The calculator will display -1,331.

Tips and Tricks for the Cube of -11

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 -11

There are some typical errors that students might make during the process of cubing a number. Let us take a look at five major mistakes that students might make:

Problem 1

What is the cube and cube root of -11?

Okay, lets begin

The cube of -11 is -1,331, and the cube root of -11 is approximately -2.224.

Explanation

First, let’s find the cube of -11. 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 (-11)^3 = -1,331 Next, we must find the cube root of -11. 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 ∛(-11) ≈ -2.224 Hence, the cube of -11 is -1,331, and the cube root of -11 is approximately -2.224.

Well explained 👍

Problem 2

If the side length of the cube is -11 cm, what is the volume?

Okay, lets begin

The volume is -1,331 cm^3.

Explanation

Use the volume formula for a cube V = Side^3. Substitute -11 for the side length: V = (-11)^3 = -1,331 cm^3.

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Problem 3

How much larger is (-11)^3 than (-10)^3?

Okay, lets begin

(-11)^3 – (-10)^3 = -331.

Explanation

First, find the cube of (-11), which is -1,331. Next, find the cube of (-10), which is -1,000. Now, find the difference between them using the subtraction method. -1,331 - (-1,000) = -331 Therefore, (-11)^3 is -331 larger than (-10)^3.

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Problem 4

If a cube with a side length of -11 cm is compared to a cube with a side length of -5 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of -11 cm is -1,331 cm^3.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -11 means multiplying -11 by itself three times: (-11) × (-11) = 121, and 121 × (-11) = -1,331. The unit of volume is cubic centimeters (cm^3), because we are calculating the space inside the cube. Therefore, the volume of the cube is -1,331 cm^3.

Well explained 👍

Problem 5

Estimate the cube of -10.9 using the cube of -11.

Okay, lets begin

The cube of -10.9 is approximately -1,331.

Explanation

First, identify the cube of -11. The cube of -11 is (-11)^3 = -1,331. Since -10.9 is only a tiny bit more than -11, the cube of -10.9 will be almost the same as the cube of -11. The cube of -10.9 is approximately -1,331 because the difference between -10.9 and -11 is very small. So, we can approximate the value as -1,331.

Well explained 👍

FAQs on Cube of -11

1.What are the perfect cubes up to -11?

The perfect cubes up to -11 are -8, -27, and -64.

2.How do you calculate (-11)^3?

To calculate (-11)^3, use the multiplication method: (-11) × (-11) × (-11), which equals -1,331.

3.What is the meaning of (-11)^3?

(-11)^3 means -11 multiplied by itself three times, or (-11) × (-11) × (-11).

4.What is the cube root of -11?

The cube root of -11 is approximately -2.224.

5.Is -11 a perfect cube?

No, -11 is not a perfect cube because no integer multiplied by itself three times equals -11.

Important Glossaries for Cube of -11

Binomial Formula: 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: 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 × 2 × 2 equals 8. Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. Multiplication Method: A process in mathematics used to find the product of numbers by combining them through repeated addition.

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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.