Question

Please help me I will really appreciate it!!!

Answer 1

`\displaystyle r=\sqrt[3]{(3V)/(4\pi)}`

The last option matches the correct solution

Explanation:

Equation Solving

We have the following equation:

`\displaystyle V=(4)/(3)\pi r^3`

And it's required to solve it for r.

Solving this equation needs to perform some operations to have the r isolated from any other variables or constants.

It can be done by conveniently operating on both sides as follows:

Eliminate the denominator by multiplying by 3:

`\displaystyle 3V=4\pi r^3`

Move
`4\pi` to the other side by dividing by
`4\pi`:

`\displaystyle (3V)/(4\pi)= r^3`

Swapping sides to have r at the left side:

`\displaystyle r^3=(3V)/(4\pi)`

Finally, take the cubic root and leave r alone:

`\displaystyle r=\sqrt[3]{(3V)/(4\pi)}`

The last option matches the correct solution