If the volume of a cube is 343x^12, what is its side length.
I’m trying to find out how to set the formula up, not for answers.
Thank you!
volume =- 343E12 what? what unit?
volume = (length)^3
343E12 =(length)^3
length = (343E12)^1/3.
for a cube , side^3 = volume
so side = (343x^12) = 7x^4
Thanks!
To find the side length of a cube given its volume, we can set up the formula as follows:
Let's assume the side length of the cube is represented by "x".
The volume of a cube is calculated by cubing the length of one of its sides. Therefore, the formula for the volume of a cube is:
Volume = (side length)^3
In this case, the volume is given as 343x^12. So, we can set up the equation as:
343x^12 = (x)^3
To solve this equation, we can take the cube root of both sides:
∛(343x^12) = ∛(x^3)
Simplifying further:
7x^4 = x
We can rearrange the equation to have all terms on one side:
7x^4 - x = 0
Now, we can factor out the common term "x" from both terms:
x(7x^3 - 1) = 0
Setting each factor equal to zero:
x = 0
7x^3 - 1 = 0
The value of x being zero does not make sense in the context of a cube's side length, so let's solve the second equation:
7x^3 - 1 = 0
Adding 1 to both sides:
7x^3 = 1
Dividing both sides by 7:
x^3 = 1/7
Finally, we can take the cube root of both sides to find the value of x:
∛(x^3) = ∛(1/7)
x = ∛(1/7)
Thus, the side length of the cube is x = ∛(1/7).