Answer:
[tex]\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
The last option matches the correct solution
Step-by-step explanation:
Equation Solving
We have the following equation:
[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]
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:
[tex]\displaystyle 3V=4\pi r^3[/tex]
Move [tex]4\pi[/tex] to the other side by dividing by [tex]4\pi[/tex]:
[tex]\displaystyle \frac{3V}{4\pi}= r^3[/tex]
Swapping sides to have r at the left side:
[tex]\displaystyle r^3=\frac{3V}{4\pi}[/tex]
Finally, take the cubic root and leave r alone:
[tex]\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
The last option matches the correct solution
