Question

What is the edge length of the cube?

Answer 1

So, `s=50 i n`

Explanation:

The volume of a cube is equal to the edge length to the third power.

`V=s^3` where `V` is the volume of the cube `(i n^3)` and `s` is the edge length `(i n).`

Here, we're given `V=125000 i n^3`

Plugging this into the formula, we get

`125000=s^3`

Take the cube root of both sides:

`root(3)(125000)=root(3)(s^3)`

The cube root of a term cubed is just that term raised to the `1st` power . As a general rule, `root(n)(x^n)=x`.

`root(3)(s^3)=s`

The cube root of `125000` is equal to `50`. In other words, if we multiply `50` by itself three times, we get `125000`; therefore, `50` is the cube root of `125000.` .

So, `s=50 i n`

Answer 2

The edge length is 50. See below

Explanation:

The cube volume formula is `V=l^3` where l is the edge.

So, in our case `125000=l^3` and from this

`l=root(3)125000= root(3)(5^3·10^3)=root(3)5^3·root(3)10^3= 5·10=50`