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 343.
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 343 can be written as 343³, which is the exponential form. Or it can also be written in arithmetic form as, 343 × 343 × 343.
To check whether a number is a cube number or not, we can use the following three methods: 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
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. 343³ = 343 × 343 × 343 Step 2: You get 40,353,607 as the answer. Hence, the cube of 343 is 40,353,607.
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 343 into two parts. Let a = 340 and b = 3, so a + b = 343 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³. Step 3: Calculate each term: a³ = 340³ 3a²b = 3 × 340² × 3 3ab² = 3 × 340 × 3² b³ = 3³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (340 + 3)³ = 340³ + 3 × 340² × 3 + 3 × 340 × 3² + 3³ 343³ = 39,304,000 + 10,404 + 3,060 + 27 343³ = 40,353,607 Step 5: Hence, the cube of 343 is 40,353,607.
To find the cube of 343 using a calculator, input the number 343 and use the cube function (if available) or multiply 343 × 343 × 343. This operation calculates the value of 343³, resulting in 40,353,607. 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 4 and 3 Step 3: If the calculator has a cube function, press it to calculate 343³. Step 4: If there is no cube function on the calculator, simply multiply 343 three times manually. Step 5: The calculator will display 40,353,607.
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 343?
The cube of 343 is 40,353,607, and the cube root of 343 is 7.
First, let’s find the cube of 343. We know that the cube of a number is x³ = y Where x is the given number, and y is the cubed value of that number So, we get 343³ = 40,353,607 Next, we must find the cube root of 343. We know that the cube root of a number ‘x’ is √x = y Where x is the given number, and y is the cube root value of the number So, we get ³√343 = 7 Hence, the cube of 343 is 40,353,607, and the cube root of 343 is 7.
If the side length of a cube is 343 cm, what is the volume?
The volume is 40,353,607 cm³.
Use the volume formula for a cube V = Side³. Substitute 343 for the side length: V = 343³ = 40,353,607 cm³.
How much larger is 343³ than 240³?
343³ – 240³ = 31,913,407.
First, find the cube of 343³, which is 40,353,607 Next, find the cube of 240³, which is 8,440,200 Now, find the difference between them using the subtraction method. 40,353,607 – 8,440,200 = 31,913,407 Therefore, 343³ is 31,913,407 larger than 240³.
If a cube with a side length of 343 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 343 cm is 40,353,607 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 343 means multiplying 343 by itself three times: 343 × 343 = 117,649, and then 117,649 × 343 = 40,353,607. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube. Therefore, the volume of the cube is 40,353,607 cm³.
Estimate the cube of 342 using the cube of 343.
The cube of 342 is approximately 40,353,607.
First, identify the cube of 343, The cube of 343 is 343³ = 40,353,607. Since 342 is only a tiny bit less than 343, the cube of 342 will be almost the same as the cube of 343. The cube of 342 is approximately 40,353,607 because the difference between 342 and 343 is very small. So, we can approximate the value as 40,353,607.
- Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer. 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, where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2, which equals 8. - Perfect Cube: A number that can be expressed as the cube of an integer. - Volume of a Cube: The amount of space occupied by a cube, calculated by raising the side length to the power of three.
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.
: He loves to play the quiz with kids through algebra to make kids love it.