Last updated on May 26th, 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 -216.
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 -216 can be written as (-216)^3, which is the exponential form. Or it can also be written in arithmetic form as, -216 × -216 × -216.
In order 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 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
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. (-216)^3 = -216 × -216 × -216 Step 2: You get -10,077,696 as the answer. Hence, the cube of -216 is -10,077,696.
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 -216 into two parts, as -200 and -16. Let a = -200 and b = -16, so a + b = -216 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-200)^3 3a^2b = 3 × (-200)^2 × (-16) 3ab^2 = 3 × (-200) × (-16)^2 b^3 = (-16)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-200 + -16)^3 = (-200)^3 + 3 × (-200)^2 × (-16) + 3 × (-200) × (-16)^2 + (-16)^3 (-216)^3 = -8,000,000 - 1,920,000 - 153,600 - 4,096 (-216)^3 = -10,077,696 Step 5: Hence, the cube of -216 is -10,077,696.
To find the cube of -216 using a calculator, input the number -216 and use the cube function (if available) or multiply -216 × -216 × -216. This operation calculates the value of (-216)^3, resulting in -10,077,696. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press - 2 1 6 Step 3: If the calculator has a cube function, press it to calculate (-216)^3. Step 4: If there is no cube function on the calculator, simply multiply -216 three times manually. Step 5: The calculator will display -10,077,696.
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.
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:
What is the cube and cube root of -216?
The cube of -216 is -10,077,696, and the cube root of -216 is -6.
First, let’s find the cube of -216. 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 (-216)^3 = -10,077,696 Next, we must find the cube root of -216 We know that 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 ∛(-216) = -6 Hence, the cube of -216 is -10,077,696, and the cube root of -216 is -6.
If the side length of a cube is -216 cm, what is the volume?
The volume is -10,077,696 cm³.
Use the volume formula for a cube V = Side^3. Substitute -216 for the side length: V = (-216)^3 = -10,077,696 cm³.
How much larger is (-216)^3 than (-200)^3?
(-216)^3 - (-200)^3 = -2,217,696.
First, find the cube of (-216), which is -10,077,696. Next, find the cube of (-200), which is -8,000,000. Now, find the difference between them using the subtraction method. -10,077,696 - (-8,000,000) = -2,217,696 Therefore, (-216)^3 is -2,217,696 larger than (-200)^3.
If a cube with a side length of -216 cm is compared to a cube with a side length of -16 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of -216 cm is -10,077,696 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -216 means multiplying -216 by itself three times: -216 × -216 × -216 = -10,077,696. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is -10,077,696 cm³.
Estimate the cube of -215.9 using the cube of -216.
The cube of -215.9 is approximately -10,077,696.
First, identify the cube of -216, The cube of -216 is (-216)^3 = -10,077,696. Since -215.9 is only a tiny bit less than -216, the cube of -215.9 will be almost the same as the cube of -216. The cube of -215.9 is approximately -10,077,696 because the difference between -215.9 and -216 is very small. So, we can approximate the value as -10,077,696.
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 × 2 × 2, which equals 8. Perfect Cube: A number that is the result of multiplying an integer by itself three times. For instance, 216 is a perfect cube because 6 × 6 × 6 = 216. Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 216 is 6, because 6 × 6 × 6 = 216.
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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