Last updated on May 27th, 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 cubes of 963.
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 963 can be written as \(963^3\), which is the exponential form. Or it can also be written in arithmetic form as, 963 × 963 × 963.
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 (\(a^3\)), 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. \(963^3 = 963 × 963 × 963\) Step 2: You get 893,700,267 as the answer. Hence, the cube of 963 is 893,700,267.
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 963 into two parts. Let \(a = 900\) and \(b = 63\), so \(a + b = 963\) Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) Step 3: Calculate each term \(a^3 = 900^3\) \(3a^2b = 3 × 900^2 × 63\) \(3ab^2 = 3 × 900 × 63^2\) \(b^3 = 63^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \( (900 + 63)^3 = 900^3 + 3 × 900^2 × 63 + 3 × 900 × 63^2 + 63^3\) \(963^3 = 729,000,000 + 153,090,000 + 10,710,000 + 250,263\) \(963^3 = 893,700,263\) Step 5: Hence, the cube of 963 is 893,700,263.
To find the cube of 963 using a calculator, input the number 963 and use the cube function (if available) or multiply 963 × 963 × 963. This operation calculates the value of \(963^3\), resulting in 893,700,267. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 9 followed by 6 and 3 Step 3: If the calculator has a cube function, press it to calculate \(963^3\). Step 4: If there is no cube function on the calculator, simply multiply 963 three times manually. Step 5: The calculator will display 893,700,267.
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 963?
The cube of 963 is 893,700,267 and the cube root of 963 is approximately 9.87.
First, let’s find the cube of 963. We know that the cube of a number is such that \(x^3 = y\) Where \(x\) is the given number, and \(y\) is the cubed value of that number. So, we get \(963^3 = 893,700,267\) Next, we must find the cube root of 963. We know that the cube root of a number ‘x’ is 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 \(\sqrt[3]{963} ≈ 9.87\) Hence the cube of 963 is 893,700,267 and the cube root of 963 is approximately 9.87.
If the side length of the cube is 963 cm, what is the volume?
The volume is 893,700,267 cm³.
Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 963 for the side length: \(V = 963^3 = 893,700,267 \text{ cm}^3\).
How much larger is \(963^3\) than \(900^3\)?
\(963^3 – 900^3 = 164,700,267\).
First, find the cube of \(963^3\), that is 893,700,267. Next, find the cube of \(900^3\), which is 729,000,000. Now, find the difference between them using the subtraction method. 893,700,267 – 729,000,000 = 164,700,267. Therefore, \(963^3\) is 164,700,267 larger than \(900^3\).
If a cube with a side length of 963 cm is compared to a cube with a side length of 63 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 963 cm is 893,700,267 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 963 means multiplying 963 by itself three times: 963 × 963 = 927,369, and then 927,369 × 963 = 893,700,267. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 893,700,267 cm³.
Estimate the cube of 962 using the cube of 963.
The cube of 962 is approximately 893,700,267.
First, identify the cube of 963. The cube of 963 is \(963^3 = 893,700,267\). Since 962 is only a tiny bit less than 963, the cube of 962 will be almost the same as the cube of 963. The cube of 962 is approximately 893,700,267 because the difference between 962 and 963 is very small. So, we can approximate the value as 893,700,267.
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 equals 8. Volume of a Cube: The space inside a cube calculated by raising the side length to the power of three. Perfect Cube: A number that is the cube of an integer. For example, 1, 8, and 27 are perfect cubes.
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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