How to solve?
Here, we just have to express r in terms of x when we are provided with the relation between x and r. We have to flip and sent it to the Right hand side.
Solution:
We have,
- [tex] \large{ \rm{x = \frac{5}{3} \pi {r}^{3} }}[/tex]
Solving it further,
[tex] \large{ \longrightarrow{ \rm{x = \frac{5}{3} \pi {r}^{3} }}}[/tex]
Taking 5/3 to the other side by dividing it,
[tex] \large{ \longrightarrow{ \rm{ \frac{3x}{5} = \pi {r}^{3} }}}[/tex]
Now, taking π to the other side by dividing it,
[tex] \large{ \longrightarrow{ \rm{ \frac{3x}{5\pi} = {r}^{3} }}}[/tex]
Cube rooting LHS to get r
[tex]\large{ \longrightarrow{ \rm{ \sqrt[3]{ \frac{3x}{5\pi} } = r}}}[/tex]
Flipping it,
[tex]\large{ \longrightarrow{ \rm{r = \sqrt[3]{ \frac{3x}{5\pi} } }}}[/tex]
So, the correct option:
[tex] \huge{ \boxed{ \bf{ \red{Option \: B}}}}[/tex]
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