Cube of -10
2026-02-28 19:15 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 -10.

Cube of -10

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 because a negative number multiplied by itself three times results in a negative number. The cube of -10 can be written as (-10)^3, which is the exponential form. Or it can also be written in arithmetic form as, -10 × -10 × -10.

How to Calculate the Value of Cube of -10

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a^3), or by using a calculator. These three methods will help you 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. (-10)^3 = -10 × -10 × -10 Step 2: You get -1,000 as the answer. Hence, the cube of -10 is -1,000.

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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 -10 into two parts, as -12 and 2. Let a = -12 and b = 2, so a + b = -10 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-12)^3 3a^2b = 3 × (-12)^2 × 2 3ab^2 = 3 × (-12) × 2^2 b^3 = 2^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-12 + 2)^3 = (-12)^3 + 3 × (-12)^2 × 2 + 3 × (-12) × 2^2 + 2^3 (-10)^3 = -1,728 + 864 - 144 + 8 (-10)^3 = -1,000 Step 5: Hence, the cube of -10 is -1,000.

Using a Calculator

To find the cube of -10 using a calculator, input the number -10 and use the cube function (if available) or multiply -10 × -10 × -10. This operation calculates the value of (-10)^3, resulting in -1,000. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press the negative sign (-), followed by 1, then 0. Step 3: If the calculator has a cube function, press it to calculate (-10)^3. Step 4: If there is no cube function on the calculator, simply multiply -10 three times manually. Step 5: The calculator will display -1,000.

Tips and Tricks for the Cube of -10

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 -10

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

Problem 1

What is the cube and cube root of -10?

Okay, lets begin

The cube of -10 is -1,000 and the cube root of -10 is approximately -2.154.

Explanation

First, let’s find the cube of -10. We know that 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 (-10)^3 = -1,000. Next, we must find the cube root of -10. 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 ∛(-10) ≈ -2.154. Hence, the cube of -10 is -1,000 and the cube root of -10 is approximately -2.154.

Well explained 👍

Problem 2

If the side length of a cube is -10 cm, what is the volume?

Okay, lets begin

The volume is -1,000 cm³.

Explanation

Use the volume formula for a cube V = Side^3. Substitute -10 for the side length: V = (-10)^3 = -1,000 cm³.

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Problem 3

How much larger is (-10)^3 than (-12)^3?

Okay, lets begin

(-10)^3 - (-12)^3 = 728.

Explanation

First, find the cube of (-10), which is -1,000. Next, find the cube of (-12), which is -1,728. Now, find the difference between them using the subtraction method. -1,000 - (-1,728) = 728. Therefore, (-10)^3 is 728 larger than (-12)^3.

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Problem 4

If a cube with a side length of -10 cm is compared to a cube with a side length of 2 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of -10 cm is -1,000 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -10 means multiplying -10 by itself three times: -10 × -10 = 100, and 100 × -10 = -1,000. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is -1,000 cm³.

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Problem 5

Estimate the cube of -9.9 using the cube of -10.

Okay, lets begin

The cube of -9.9 is approximately -1,000.

Explanation

First, identify the cube of -10, The cube of -10 is (-10)^3 = -1,000. Since -9.9 is only a tiny bit less negative than -10, the cube of -9.9 will be almost the same as the cube of -10. The cube of -9.9 is approximately -1,000 because the difference between -9.9 and -10 is very small. So, we can approximate the value as -1,000.

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FAQs on Cube of -10

1.What are the perfect cubes up to -10?

The perfect cubes up to -10 are -1, -8, and -27.

2.How do you calculate (-10)^3?

To calculate (-10)^3, use the multiplication method, -10 × -10 × -10, which equals -1,000.

3.What is the meaning of (-10)^3?

(-10)^3 means -10 multiplied by itself three times, or -10 × -10 × -10.

4.What is the cube root of -10?

The cube root of -10 is approximately -2.154.

5.Is -10 a perfect cube?

No, -10 is not a perfect cube because no integer multiplied by itself three times equals -10.

Important Glossaries for Cube of -10

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. Perfect Cube: A number that can be expressed as the cube of an integer. Cube Root: A number that, when multiplied by itself three times, gives the original number. It is denoted by the symbol ∛.

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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.