Question

Please help me I will really appreciate it!!!

Answer 1

Answer:

$\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}$

The last option matches the correct solution

Step-by-step explanation:

Equation Solving

We have the following equation:

$\displaystyle V=\frac{4}{3}\pi r^3$

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 $4\pi$:

$\displaystyle \frac{3V}{4\pi}= r^3$

Swapping sides to have r at the left side:

$\displaystyle r^3=\frac{3V}{4\pi}$

Finally, take the cubic root and leave r alone:

$\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}$

The last option matches the correct solution